The 27-year-old lasted just 51 minutes during his side's 3-1 victory over Manchester United last weekend, being forced off early in the second half after landing awkwardly.
Janmaat, who only joined Watford from Newcastle United last month, has started the club's last two games but is now not expected to play again until November.
"We really didn't need this now as it is quite a bad injury. It could be a shoulder fracture - he has been checked - and we will know how long he will be out for in the next few days," Watford boss Walter Mazzarri told reporters.
"As you know, we count on him a lot. He was progressing, and started playing in the squad the way I wanted him to play."
Janmaat's fellow defender Jose Holebas is also a doubt for Monday night's match against Burnley at Turf Moor.