Despite controlling large periods of the game and creating the clearer opportunities, the Tanzanian giants were unable to break down a well-organised and disciplined Somali defence.
The result leaves both teams with one point from their first outing.
Earlier in the day, Jamus SC of South Sudan produced a major upset by defeating defending champions Singida Black Stars 2-0, moving them to the top of Group B.
Group B standings (after Matchday 1)
Simba will look to get their campaign on track when they face group leaders Jamus on Tuesday, 28 July.
