Jakub Piotrowski put Poland 1-0 up in the 38th minute of the game at the Polish capital's National Stadium, but Tomáš Souček equalized four minutes into the second half.
Neither the home side nor the visitors managed to score during the remainder of the game, which was played in front of a crowd of 56,310, Polish state news agency PAP reported.
The Poles, captained by Barcelona striker Robert Lewandowski, failed to impress and will now be looking to secure a spot in Euro 2024 through playoffs in March.
Poland are ranked 31st worldwide by football's governing body FIFA, while the Czech Republic are No. 41 in the FIFA table.
Poland won 11 points from eight matches in their qualifying Group E, which also included Albania, Moldova and the Faroe Islands.
The Euro 2024 tournament will be held from June 14 to July 14 in 10 cities in Germany, with the final played at Berlin's Olympiastadion.
Source: IAR, PAP, Polsat Sport