The forint, the zloty and the Czech crown slipped 0.1 percent versus the euro by 0908 GMT.
The decline in currencies and stocks remained muted, even though the IMF cut its growth forecast for Germany, the region's main export market.
"The new report reads only that the growth should remain sound, despite significant downward revision of the German GDP growth pace (from 1.9% to 1.3% in 2019)," Warsaw-based Santander bank analysts said in a note.
A drop in Poland's annual retail sales growth to 4.7 percent in December confirmed that the region's robust growth also might slow. The Polish economy grew by about 5 percent last year.
Hungary's 10.4 percent November annual gross wage growth figure, however, indicated that incomes continue to rise in the region, reducing its gap with richer Western Europe.
"Definitely, we are less dependent on the Germans than five or 10 years ago, but their slowdown story must be watched," said Lajos Torok, analyst of Equilor brokerage in Budapest.
The mood among German investors improved unexpectedly in January, a survey showed on Tuesday, suggesting that the growth prospects of Europe's largest economy are brightening.
Investors in the region will also be watching the European Central Bank's reaction to slowdown fears after its meeting on Thursday.
If European growth concerns weaken the euro against the dollar, that can pull down Central European currencies, too. Or they might get support if the ECB's reaction is to postponing monetary tightening, market participants said.
The forint, trading at 318.1 against the euro, stayed near the 7 1/2-month high it reached after National Bank of Hungary Deputy Governor Marton Nagy said last week policy might tighten if annual core inflation rose to or above 3 percent.
The Czech crown, buoyed by expectations central bank rate hikes would continue, could get additional support from the government's plan to renew bond sales in February, Raiffeisen analyst Eliska Jelinkova said in a note.
Budapest's stock index was steady after retreating from one-year highs on Monday.
The shares of small holding company Est Media shed 8.5 percent on Tuesday, or a total of over 30 percent, after the death of major shareholder Andrew G. Vajna on Sunday.
It gave up all the gains that it posted in October when Vajna, a renowned film producer and media entrepreneur, bought a 5 percent stake in the firm, triggering hopes for further investments.