Sonia Bompastor's side controlled much of the contest at the Nordic Wellness Arena but could not find a breakthrough against a resilient Swedish defence and an outstanding performance from goalkeeper Jennifer Falk.
Chelsea thought they had taken the lead in the fifth minute when Wieke Kaptein found the net from a corner, but the goal was ruled out following an infringement involving Lexi Potter and the goalkeeper.
The visitors had another goal disallowed in the 28th minute after Melvine Malard finished brilliantly, only for the assistant referee to raise the flag for offside.
Chelsea waste several opportunities
The Blues continued to press after the interval, with Ellie Carpenter coming close to breaking the deadlock early in the second half.
However, Falk produced an excellent save to deny the Australian defender.
Chelsea kept searching for a winner, but their efforts were repeatedly frustrated by Häcken's defensive organisation and goalkeeping.
The visitors also struck the crossbar twice, while goalkeeper Livia Peng made important saves at the other end to prevent the hosts from snatching a late victory.
Despite registering 32 shots and enjoying 691 passes, Chelsea were unable to convert their dominance into goals.
Chelsea maintain unbeaten European record
The result means Chelsea remain unbeaten and have yet to concede a goal in their opening four matches of the 2026/27 Women's Champions League league phase.
The London club moved up to second place in the standings with 10 points, keeping themselves firmly in contention for automatic qualification to the quarter-finals.
Chelsea will now turn their attention to a major Women's Super League clash against Manchester City on Saturday, 14 November.
Full-time: BK Häcken Women 0-0 Chelsea Women
Competition: UEFA Women's Champions League, 2026/27 league phase
Venue: Nordic Wellness Arena, Gothenburg, Sweden