The warning, issued after the bank's decision to keep borrowing costs unchanged at 4.5 percent, reduced investors' appetite for the Mexican peso, which fell half a percent to 12.6565 per US dollar.
"The peso reacted by depreciating," said Ezequiel Aguirre, a strategist at Bank of America in New York.
"If the cut materializes, it will lower the 'carry'," he added, referring to the so-called carry trade in which investors borrow money in lower-yielding currencies such as the US dollar or the Japanese yen to buy assets denominated in higher-yielding currencies such as the Mexican peso.
Mexican rates also sold off after the central bank's statement, which was an about-face from the previous guidance suggesting an interest rate rise was coming.
The yield on Mexico's 2-year interest rate swap , one of the most popular vehicles to bet on monetary policy, bid nearly 12 basis points lower, on track for its biggest one-day drop since last May.
Despite the strong market reaction, many analysts consider it unlikely that the central bank will actually lower interest rates soon, just like it did not increase them after its previous warning.
"We believe that the Mexican central bank will remain neutral in the coming meetings and no change in interest rate will be implemented," Barclays analysts Marco Oviedo and Bruno Rovai wrote in a research note.
"This balance of risks - higher downside global risks and lower domestic inflation - is allowing Banxico to signal to the markets that it is ready to use monetary policy to support growth. However, we believe that additional economic growth data is needed to trigger such action."
Other Latin American currencies also weakened after a disappointing earnings outlook from chipmaker Intel overshadowed stronger-than-expected economic data from China.
The Brazilian real dropped 0.2 percent to 2.0440 per US dollar, nearing the upper limit of the narrow range of 2.0-2.05 per dollar where it has been trading since the end of 2012.
Analysts bet, however, that the Brazilian central bank will not allow the real to weaken much past 2.05 per dollar for fear of inflation pass-through.
Those concerns increased after the bank's board said, in a statement issued after their rate-setting meeting on Wednesday night, that the inflation outlook worsened in the short term, while economic activity continues to disappoint.
The central bank's "post-decision communiqué acknowledges the growing challenges faced by monetary authorities, which in our view indicates that the central bank will keep its tight grip on the exchange rate at least through the inflationary hump expected in the first quarter of 2013," JPMorgan's analysts said in a note to clients.