The center-right government had planned to float its 37-percent stake in BGZ, which is controlled by Dutch Rabobank, in July.
"After the 20th (of June) we will meet with the BGZ investors to decide whether this is a good moment. If not, then we'll put off the decision until September," Treasury Minister Aleksander Grad said in a radio interview.
"The market is in such a state right now, especially for financial institutions, that we should consider whether today is a good time (for an IPO)," he added.
Warsaw's listed banks are down 21 percent this year, as wider concerns about the global financial sector overshadowed their strong growth prospects.
The sale of the state stake in BGZ, a key part of this year's privatization plan, was expected to net up to 1 billion zlotys ($457.9 million).
Grad also said the planned IPO of energy group Enea would likely take place in August or September, instead of the planned July.
Pointing to potential troubles with further privatization plans, business daily Parkiet reported that chemicals group Tarnow would likely fall short in raising the planned $141 million from its IPO. It expects to start trading on June 30.
The newspaper said many funds baulked at the IPO price of 19.50 zlotys per share, and several state-owned companies stepped in to buy Tarnow shares. The company will announce the number of shares sold later on Wednesday.