An unusual surge of short-term lending by cash-rich companies is raising concerns on Wall Street that a period of market unrest may lie ahead.

Investors such as money-market funds and banks are parking over $1 trillion in spare cash overnight at the Federal Reserve in exchange for securities. That’s the most on record since the Fed opened the facility for so-called reverse repurchase agreements in 2013.

The scale of this flood has some analysts warning that the markets for short-term funding appear to be vulnerable to disruption.

The worry isn’t new. The Fed said in its last meeting it would establish two new permanent facilities to guarantee investor access to a related market known as repo, in which financial firms borrow cash using securities such as Treasury debt as collateral. The decision aims to brace markets against volatility that could hit when the central bank begins tightening financial conditions in coming years.

Short-term debt sits at the intersection of markets and the economy, and as such the functioning of these markets is central to the health of the U.S. recovery and the broad advance in prices of stocks, bonds and other assets.

While few investors believe repo and reverse markets are imminently vulnerable to the kind of breakdown that characterized the 2008 crisis, the sensitivity of these markets to policy changes and economic developments is leaving many portfolio managers on edge. That’s doubly so at a time of record U.S. bond issuance, ultralow interest rates and a booming economic recovery that has sent inflation to its highest level in years.

“Repo is a heavily traded market with an enormous amount of turnover on a daily basis and it represents the bedrock of the Treasury market,” said Michael de Pass, global head of U.S. Treasury trading at Citadel Securities. “It is foundational to the functioning of financial markets.”

Treasury repurchase agreements are the financial markets’ main mechanism for moving cash from those who have it to those who need it. Traders say it’s the No. 1 market they watch to gauge short-term bond markets. In a typical transaction, a bank or hedge fund posts Treasurys as collateral to borrow cash that is often then used to finance other trades. The borrower pays the lender interest at a stated rate when it “repurchases” the collateral at the end of the loan.

Though seemingly obscure, these markets are crucial not only to investors and bankers but also to policy makers. The Fed uses repo to control short-term interest rates, a practice that emerged after the regulatory overhauls and quantitative easing that followed the financial crisis. Reverse repo helps set the floor on overnight interest rates by preventing them from falling below zero, while the repo market helps set a ceiling to keep them from soaring when funding strains hit financial firms, the way they did in March 2020.

“It helps with policy implementation,” said Darrell Duffie, a professor of finance at Stanford University’s Graduate School of Business. “If there were no overnight reverse repurchase facility, the repo rate would fall and pull other short-term market rates lower—potentially moving the funds rate below the Fed’s target range.”

Despite the market’s evident importance, it isn’t always clear what the dynamics are beneath the surface. Analysts describe the $5.1 trillion repo market as opaque, with little public information on trades, collateral or even participants for a large chunk of transactions, and they say that some aspects of it have barely changed since its inception in the 1980s.

Disruptions in the 2008 crisis and again two years ago reinforced the sense that the market was subject to many competing, often unseen forces. Some investors blamed the turmoil on shrinking reserves at the Fed, dealers holding more Treasurys as a consequence of greater federal borrowing and postcrisis regulations increasing the cost of repo transactions and forcing out smaller dealers. These rules have also limited how much large dealers may lend.

Michael Feroli, chief U.S. economist at JPMorgan, said repo markets weren’t intended as a central bank tool to control short-term interest rates, but changes in market structure over the past decade have transformed repo rates into a major influence on the Fed’s benchmark federal-funds rate.

“Banks’ desire to hold reserves, regulatory issues affecting the pipes and a withered fed-funds market—a lot of these things weren’t there several years ago, but they are now,” Mr. Feroli said.

The flood of cash into reverse repo this summer seems to stem from the Fed’s decision to raise the interest rate it pays on these loans to 0.05% to eligible users from 0%. Though an increase in the use of the reverse repo facility was predictable with the payout rising, analysts said they were surprised by the speed with which firms rushed to move their money into reverse repo from other short-term investments such as Treasury bills and commercial paper.

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Bill Nelson, chief economist at BPI and a former top Fed staffer, said heavy usage of the reverse repo facility increases the systemic importance of money market mutual funds, a sector the Fed sees as a financial stability risk. It’s a sign that financial markets continue to change and that investors and policy makers must redouble their efforts to keep up.

“From its conception up to the great financial crisis, the Fed borrowed mostly from the public in the form of currency. After the crisis. the Fed has also been borrowing from banks in the form of reserve balances,” said Mr. Nelson. “Since March, the Fed is borrowing heavily from money funds.”

Write to Julia-Ambra Verlaine at Julia.Verlaine@wsj.com