Arshavin was included in an attack-minded Arsenal line-up
Arsenal's hopes of qualifying for the Champions League were dealt another severe blow as Fulham inflicted the Gunners' fifth successive league draw.
Andrew Johnson went close for Fulham before Robin van Persie's close-range header was saved by Mark Schwarzer.
Van Persie was foiled by a superb Schwarzer when in on goal and headed against the post after half-time.
Johnson glanced just wide from close range before Schwarzer denied Abou Diaby and Andrey Arshavin late on.
A draw was the least Fulham deserved for a performance full of attacking ambition and dogged defensive resilience. Despite not winning on their travels all season, they have now held Liverpool, Aston Villa and Arsenal.
The visitors' point is only their third of all time away at Arsenal, where they have never won, and takes them up to seventh after Wigan were beaten at Chelsea.
Arsenal are five points adrift of fourth-place Aston Villa, having played a game more, and just two points above sixth-place Everton.
Arsene Wenger's men have now drawn four league matches 0-0 for the first time since October 1993.
There must be serious concerns for Wenger, whose side appears devoid of attacking invention and a cutting edge in front of goal.
For Wenger, the likes of Cesc Fabregas, Theo Walcott, Tomas Rosicky, Eduardo and Emmanuel Adebayor cannot return soon enough.
Arsenal last scored a home league goal on 10 January and, perhaps with that in mind, Wenger named Van Persie, Arshavin, Carlos Vela and Samir Nasri in an attack-minded line-up.
But is was Fulham, inspired by midfielders Danny Murphy and Simon Davies and centre-half Brede Hangeland, who made by far the brighter start.
Wenger concerned about fourth-place chase
Manager Roy Hodgson restored a fit-again Johnson to his starting XI and, partnered by the in-form Bobby Zamora, he caused Arsenal's centre-halves no shortage of problems early on.
Davies had already evaded the hosts' offside trap and fired over from 20 yards before Johnson twice escaped the attentions of Kolo Toure and William Gallas inside the opening 10 minutes.
The striker scuffed his first effort across goal and well off target but, after turning Toure, flashed his second marginally wide of Manuel Almunia's left-hand post.
With the home crowd beginning to grow restless, Arsenal were quick to respond with an attack of their own and Van Persie saw a powerful header from Arshavin's cross tipped over the crossbar by Schwarzer.
Arsenal's lack of cohesion and predictable attacking game-plan allowed Fulham to grow in confidence and when Gallas could only clear Zamora's centre to Danny Murphy, the midfielder's drive from the edge of the penalty area fizzed just over.
We matched Arsenal - Hodgson
Murphy's shot seemed to remind Arsenal that they were in a game and, after a neat move that ended when Nasri failed to get his shot away, they should have opened the scoring.
Arshavin sent Van Persie through on goal with an exquisite slide-rule pass but the Dutchman's right-footed strike was blocked by an on-rushing Schwarzer.
Arsenal started the second half in determined fashion and after Nasri shot narrowly wide, Van Persie headed onto the roof of the net from the Frenchman's corner.
Van Parsie came even closer soon after as his flicked header from Bacary Sagna's centre clipped the far post, but Fulham were by no means being outplayed.
Clint Dempsey and Johnson almost broke through on the Arsenal goal and Johnson saw a shot deflected onto the roof of the net before flicked Frederik Stoor's cross wide from an unmarked position six yards out.
Schwarzer repelled Diaby's header and Arshavin's fierce drive as Arsenal were frustrated and left the field to a chorus of boos.
Arsenal manager Arsene Wenger:
"We had chances to score and so did they, it was an open game. And it finished with a result that we did not want as we have dropped two points.
"We are not scoring goals and the offensive confidence of the team is not high and as a result the players are becoming a little anxious.
"The fans are frustrated and so are we are.
"We have to take the result on the chin and continue to fight."
Fulham manager Roy Hodgson:
"There were times in the game when we played to our full potential - it was as good as it gets from us.
"We were a constant threat and we carved out many opportunities. Arsenal are an offensive side at home and we matched them.
"We were well organised and the shape of our team was good."
Almunia, Sagna (Eboue 70), Toure, Gallas, Clichy, Arshavin, Denilson, Diaby, Nasri, Van Persie, Vela (Bendtner 63).
Subs Not Used: Fabianski, Ramsey, Song Billong, Djourou, Gibbs.
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