However, despite failing to ensure progress on the night, Arsenal are still well placed to advance as they top the standings with eight points from four games, with Marseille second on seven.
Borussia Dortmund have four and Olympiakos three after Dortmund, who visit Arsenal in their next match, won the group's other game 1-0.
Tuesday's match was something of a repeat of the team's Velodrome meeting last month - without the drama of Arsenal's late winner.
The Londoners, recovering from a slow start to the season with five successive wins, were lacklustre on a night manager Arsene Wenger started with Robin van Persie, the hat-trick hero of Saturday's 5-3 win at Chelsea, on the bench.
He came on for the later stages but even he failed to find the spark that would have ignited the home side's performance.
Knowing a point would keep each side on course, neither were prepared to risk too much, with the result that neither took control of the game and neither created many chances.
Marseille, starting brightly with an effective 4-4-2 formation with either Andre Ayew or his brother Jordan joining Loic Remy up front, could have taken the lead after six minutes when Andre stabbed the ball just wide of Wojciech Szczesny's left-hand post after a good move involving Remy in the build-up.
Theo Walcott had Arsenal's first chance after 10 minutes when he hit a low drive wide of Steve Mandanda's right-hand post, but with Souleymane Diawara doing an effective job in the front of his back four, Marseille limited Arsenal's attacking options with some degree of defensive authority.
Aaron Ramsey, scorer of Arsenal's last-gasp winner in the first match two weeks ago, had two good chances but failed to convert either of them, sending the ball wide from the first when he was close to goal and taking too long to strike and saw the ball cleared with the second.
There were few chances after the break either as the match petered out to a forgettable draw that probably satisfied both coaches.
"We need to be winning our home matches, but we were solid at the back and it's a point," Arsenal winger Theo Walcott told Sky Sports.
"Saturday did take a lot out of us but they are a strong side and we found it quite tough out there."
Marseille's Nicolas Nkoulou told Canal Plus: "We had to be solid tonight. We could even have won this game.
"Nothing is done yet but it's a good result. We hope it's going to be enough."
Champions League results
Group E: Valencia (Spain) 3, Bayer Leverkusen (Germany) 1; Genk (Belgium) 1, Chelsea (England) 1.
Group F: Arsenal (England) 0, Marseille (France) 0; Borussia Dortmund (Germany) 1, Olympiakos (Greece) 0.
Group G: Zenit St. Petersburg (Russia) 1, Shakhtar Donetsk (Ukraine) 0; APOEL (Cyprus) 2, FC Porto (Portugal) 1.
Group H: BATE Borisov (Belarus) 1, AC Milan (Italy) 1; Viktoria Plzen (Czech Republic) 0, Barcelona (Spain) 4.
