Both players had to be withdrawn during Wednesday night's home 1-1 draw with Fulham.
Brady was introduced from the bench to replace Gudmundsson after the Icelandic midfielder suffered an injury just before half time. However, Brady lasted only 25 minutes before he was then taken off himself.
The pair are set to undergo scans on their respective knocks ahead of Burnley's game against the Baggies at Turf Moor on Saturday but Dyche is not optimistic.
"I'll find out more by tomorrow morning, we're waiting 24 hours just to settle things down, but it doesn't look great with Johann and Robbie going off," said the Burnley boss at his pre-match press conference on Thursday.
"We'll find out more in the next 24 hours and we'll probably get them scanned just as a precaution.
"We don't think either is drastic but we keep getting these knocks in this heavy schedule of games and it is affecting us.
"Gudmundsson has looked free flowing actually in his body and his running and the physical performances, so that was a bit of a disappointment.
"He did have tightness in it last week and we got him off quick. Luckily last night he got his hand up quick and we got him off quick. We hope that it's better news but it will probably need a settling down period."
Some good news for Dyche will see the return of captain Ben Mee against West Brom after the central defender had to sit out the Fulham game under concussion protocols.
Former Baggies loanee Matej Vydra could also come back into contention should he come through training unscathed.
However, Dyche expects Dale Stephens and Erik Pieters to remain out while it will be a close call once more on whether Chris Wood is available.
"Ben Mee comes back. Matej Vydra, as long as he comes through training should be back in and around it. We've got a couple back, couple out. It's trying to juggle the pack," said Dyche.
"I don't think Dale Stephens will be available. Erik, I doubt it as well, but we'll see. Woody will be a close one, but yet again I'm having to make judgements on these players.
"It's not the perfect scenario but a better scenario than we've had for a while now so we're adapting to it."