The 32-year-old started the contest with the Red Devils on right side of the offensive-minded trio behind striker Zeki Amdouni, who scored in the draw with Nottingham Forest during the Clarets' previous match.
Gudmundsson was starting his fourth-straight game for Burnley at the opening stages of the 2023-24 term after featuring from the off in Premier League matches against the likes of Tottenham Hotspur and Forest earlier in the month.
Following a promising beginning to the match for the hosts at Turf Moor, Gudmundsson was forced off after just 18 minutes, being replaced by Genk loanee Mike Tresor.
Burnley boss Vincent Kompany provided an update on the midfielder's condition in his post-match press conference, and the Belgian was hopeful that the issue would not leave him without the player for too long.
"I hope it is just cramp or a little bit of tiredness in his muscle," said Kompany when questioned about the injury to Gudmundsson following the full-time whistle in Lancashire.
Although the Burnley boss did not specific the type of injury, it is understood that the 32-year-old had strapping applied to his left calf as he watched the remainder of the match from the bench alongside his teammates.
The rest of the game in Lancashire saw the hosts dominate possession but ultimately end up empty handed due to a moment of quality from Bruno Fernandes, who fizzed a controlled volley past James Trafford from a long-range Jonny Evans pass.
It is expected that Gudmundsson will miss out on his side's trip to Salford City in the third round of the EFL Cup on Tuesday night, with Kompany set to make wholesale changes to the XI which started against Erik ten Hag's team.
Jacob Bruun Larsen and Jay Rodriguez are players who could be handed a starting berth in the cup clash at The Peninsula Stadium, as the Clarets look to secure their passage in the last 16 of the competition.
Focusing on the Premier League, Burnley are sitting 19th in the top-flight standings after five matches, having collected just a single point since their promotion from the Championship.
It remains to be seen whether Gudmundsson will be available when the Clarets travel to Newcastle United next Saturday in the league, with Eddie Howe's Magpies fresh from their 8-0 demolition of Sheffield United at Bramall Lane.
The Iceland international made the switch to Turf Moor from Charlton Athletic in the summer of 2016, and has since featured in over 200 games for the club, scoring 13 goals.