By Caitlin Ostroff and Anna Isaac

The cost of borrowing Turkish lira spiked on Tuesday, highlighting how the currency, once a darling of emerging-market investors, has lost appeal.

The interest rate attached to so-called swap transactions, which allow one party to obtain lira for a short period in exchange for dollars, reached 1,000% in annualized terms on offshore markets, according to analysts and traders.

The exorbitant rate wasn't a reflection of high demand for the lira, analysts said, but rather of how the Turkish currency's offshore market has become dysfunctional.

The spike, which began overnight, was likely the result of a bank or investor trying to buy lira after having shorted it, or bet on its weakening, and being unable to buy the currency back, said Timothy Ash, senior sovereign strategist covering emerging markets at BlueBay Asset Management.

The lack of liquidity, or ease with which traders can buy or sell, stems from Turkish authorities making it more difficult for local banks to provide lira to foreign banks. This has decreased access to the lira, pushing up borrowing rates to obtain it.

"They've limited that market massively," Mr. Ash said. "The offshore market is broken."

The overnight spike heightened investor nervousness over the lira's future trajectory. Investors are worried that Turkey's central bank, which sold billions of dollars in recent months in a bid to prop up the lira, is running low on options to curb volatility in its currency. The central bank used its own reserves, but also dollars borrowed from domestic banks, to buy the lira. As a result, it owes more foreign currency to the banks than it currently has in its coffers.

The central bank has said it has adequate reserves.

A textbook lever to support the lira, which has lost more than 14% against the dollar so far this year, would be to increase the central bank's benchmark lending rate. But Turkey's President Recep Tayyip Erdogan has instructed the country's financial authorities to keep interest rates low and boost lending to households and businesses to fuel economic growth.

At home, analysts said that the central bank could continue to tap into the pool of dollars credited on the books of Turkish lenders, which stands at about $230 billion, as long as the banks don't express an immediate need for them.

Abroad, however, they said that the shrinking offshore lira market would soon create problems for Turkey itself. Initially, Turkish authorities sought to make it harder for investors and banks to bet on the lira weakening, helping limit the lira's slide against the dollar this year. But the restrictions have also hindered the activities of foreign portfolio investors willing to buy assets in lira, as well as of direct investors in Turkey, they said.

"It's not a sustainable story," said Charles Robertson, chief economist at Renaissance Capital. "You can't do this without creating problems in the function of financial markets."

Write to Caitlin Ostroff at caitlin.ostroff@wsj.com and Anna Isaac at anna.isaac@wsj.com