Both sides were making their European bow for the campaign and neither were able to hit the ground running at 3Arena, before Hammarby settled into a rhythm after more than half an hour.
Paulos Abraham and Hampus Skoglund both dug out goalbound efforts, yet both were denied by Martin Delavalee in the Charleroi goal.
Despite less possession, the Allsvenskan runners-up had seven shots to Chareloi's one in the opening 45 minutes, as the winners of the Jupiler Pro League's European play-off offered no real test for Bajen goalkeeper Warner Hahn.
Hahn was finally forced into action on the hour mark, dealing with an Etienne Camara strike. That chance sparked Hammarby into life, but neither Shaquille Pinas nor Victor Eriksson could force a breakthrough.
10 minutes from time, a section of the home crowd were on their feet when Nahir Besara tried his luck from a free-kick out wide, only for the ball to narrowly clear the crossbar.
The home side threw everyone forward late on and had a penalty claim waved away in a heated end to the game, but no late winner in Stockholm means it will be all to play for in the return leg in Belgium next Thursday.