The Gunners were held to a frustrating goalless draw by the Tigers at Emirates Stadium on Saturday lunchtime as they failed to find the net against Steve Bruce’s men.
Arsenal are unbeaten in 15 rounds of the FA Cup, while Watford last reached the sixth round of the competition as part of a run to the semi-finals in 2007.
Manchester United, meanwhile, will welcome West Ham United to Old Trafford in the quarter-finals if they beat Shrewsbury Town in the fifth round on Monday night.
Chelsea, who were 5-1 winners over Manchester City in the fifth round at Stamford Bridge on Sunday, face a trip to Everton for a place in the semi-finals.
Everton v Chelsea
Arsenal or Hull City v Watford
Shrewsbury or Man Utd v West Ham
Reading v Crystal Palace
Crystal Palace will travel to Reading after the Eagles beat Tottenham 1-0 at White Hart Lane on Sunday.
The FA Cup quarter-final ties will be played between 11 and 14 March 2016.
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