Both sides headed into the Group C encounter at the Stadion Petrovsky having earned wins in the opening matchday, Zenit impressively overturning Benfica in Lisbon while Monaco beat Bayer Leverkusen.
However, neither team was able to find the inspiration that helped to their respective opening victories in a dour affair in St Petersburg.
Leonardo Jardim's Monaco had the better of the play for the majority of the contest but were unable to find a way through Zenit goalkeeper Yuri Lodygin, who produced a string of saves to preserve the impressive streak for Andre Villas-Boas' side.
The result leaves both clubs on four points heading in to the third round of fixtures in three weeks' time.
Zenit enjoyed a better share of possession in the second half but the final ball continued to desert them as the hosts' attack was frustrated by a stern Monaco defence.
Villas Boas' men did finally force Monaco goalkeeper Danijel Subasic into a save with 25 minutes to play, but Nicolas Lombaerts could only direct his header from Hulk's corner directly at the Croatian shot-stopper.
Monaco pressed for the late winner their strong away performance perhaps deserved, yet Ferreira Carrasco's chance proved to be the last meaningful opportunity of the contest as the spoils were shared.
