Guidolin was not present at the Barclays Premier League fixture after being admitted to a London hospital with a chest infection.
The 60-year-old Italian had been ill the previous week when he missed two days of training and failed to fulfil his media duties before Sunday's game at Tottenham.
Guidolin was referred to a respiratory specialist in London hours before the Arsenal game, and no date has been given for when he will leave hospital.
"Francesco remains comfortable in hospital and is receiving excellent care and treatment," a Swansea statement read.
"He is making good progress and is in good spirits following (Wednesday night's) result at Arsenal.
"The club is in close contact with Francesco and his consultant and his progress is being reviewed on a regular basis.
"No release date from hospital has been confirmed at present."
First-team coach Alan Curtis guided the side in Guidolin's absence at the Emirates Stadium, where a 2-1 win eased the Swans' relegation worries.
Goals from Wayne Routledge and captain Ashley Williams moved Swansea six points above the drop zone ahead of Saturday's crunch game with fellow strugglers Norwich.
Curtis, who had a six-week spell in charge between Garry Monk's December departure and Guidolin's appointment, is set to oversee the team again when the Canaries visit the Liberty Stadium this weekend.
Source : PA
Source: PA