Sofyan Amrabat of Morocco and Croatia's Luka Modric
Only four players from their final defeat by France in 2018 started this game and they lacked an attacking spark throughout, but came closest through Nikola Vlasic's toe-poked effort.
Morocco were impressive, but failed to create clear-cut opportunities.
Belgium play Canada in the other Group F game at 19:00 GMT on Wednesday.
Croatia, who are 12th in Fifa's world rankings, dominated possession as expected, but they were unable to create opportunities or break down Morocco, who have only lost two of their past 40 games across three years.
The best chance of a match that had only two shots on target from each side came in first-half stoppage time, when a left-wing cross was diverted towards goal by Vlasic, but the midfielder on loan at Torino from West Ham was denied by the right leg of Yassine Bounou, who spread himself to close down the angle.
Morocco, who are ranked 22nd, came closest when Noussair Mazraoui followed in a deflected shot and saw a back-post header saved.
Paris St-Germain full-back Achraf Hakimi also tested Dominik Livakovic, but the Croatia keeper dealt with his dipping, swerving 35-yard strike with ease.
It was a game largely played in the middle third of the pitch, with both sides potentially wary of losing and damaging their chances of progressing to the knockout stages from a group that also contains Belgium and Canada.
The goalless draw is the third of this World Cup, after Denmark's opener against Tunisia and Poland v Mexico on Tuesday. There was only one in the entire 2018 tournament in Russia.
Croatia will play Canada in their next match on Sunday (16:00 GMT kick-off), while Morocco face Belgium on the same day (13:00).
-- Courtesy of BBC Sport