Murray was confined to his hotel room with a stomach bug during the draw on Thursday but the Wimbledon champion is likely to line up against Seppi in Friday's second singles match, when he will be looking for his sixth consecutive win against the Italian.
''Andy's got some sort of virus which has made him feel pretty poorly over the last 24 hours in particular,'' Britain captain Leon Smith said. ''It is important to give him a lot of rest and recovery. That's why he didn't attend the draw, to spend time with the doctor and stay at the hotel away from the rest of the group.
''Hopefully he can be fit and play a big part in the weekend, which I'm sure he will. He's a fighter and obviously desperate to play so looks like he will be OK.''
Despite his illness, Murray will still be the favorite against Seppi, who - at no. 34 - is ranked 26 places below the two-time Grand Slam champion.
''It's going to be a very difficult match,'' Seppi said. ''He's a great player. The last matches I played against him, I always lost so I have to do better. I have to try and play my best game, very aggressive and hopefully I can beat him.''
Italy will be relying heavily on Fognini's fine form as it attempts to reach the final four for the first time since 1998.
The charismatic Fognini is currently at a career-high ranking of No. 13, after winning three singles titles on clay within the past nine months. He said he has fully shaken off a left leg injury he picked up in the quarterfinal defeat to Rafael Nadal in Miami.
''I feel great,'' said Fognini. ''I was a little bit tired, felt some pain in the legs, but now I feel much better. I have had more than one week to recover and hopefully Friday is going to go the right way
Colin Fleming and Ross Hutchins are set to face Simone Bolelli and Paolo Lorenzi in Saturday's doubles.