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.
Monaco almost went ahead as early as the third minute when Dimitar Berbatov was denied from close range by Lodygin after meeting a pull-back from Lucas Ocampos.
Nabil Dirar then narrowly fired over the crossbar with a spectacular scissor-kick volley from long range before Ocampos headed a Joao Moutinho free-kick wide at the near post as the visitors dominated the early stages.
Zenit did manage to weather the early storm but their lack of a goal threat was evident throughout a first half which was low on excitement for the most part.
Ocampos looked the player most likely to break the deadlock and only a flying save from Lodygin prevented him from doing so in the 43rd minute.
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.
Having replaced Berbatov, Yannick Ferreira Carrasco went close to punishing Zenit for their lack of attacking threat, the winger shooting narrowly wide on the rebound after seeing his initial effort well saved by Lodygin.
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.
The principality club will next host Benfica while Zenit visit the BayArena to take on Leverkusen.
