Ion Nicolaescu put Moldova 1-0 up in the 26th minute of the game at the Polish capital's National Stadium, but Karol Świderski equalized in the 53rd.
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 around 51,670.
The draw followed the Polish team's 2-0 away win over the Faroe Islands in its previous qualifier three days earlier under its new coach Michał Probierz.
The Poles, captained by Napoli midfielder Piotr Zieliński, played Sunday's match without their star striker Robert Lewandowski, who had been ruled out by an ankle injury.
Poland are ranked 30th worldwide by football's governing body FIFA, while Moldova are No. 159 in the FIFA table.
After seven rounds of fixtures, Poland are third in their qualifying Group E, with 10 points, behind Albania and the Czech Republic, having played one match more than its rivals.
The Poles will take on the Czech Republic in their last qualifier in Warsaw on November 17.
The Euro 2024 tournament will be held from June 14 to July 14, 2024 in 10 cities in Germany, with the final played at Berlin's Olympiastadion.
Poland reached the last 16 of last year's World Cup in Qatar before being eliminated by eventual runners-up France.
Probierz took over as Poland manager in the middle of last month.
(gs)
Source: IAR, PAP