The Chelsea defender stalked off, accompanied by physio Gary Lewin, during the session at Hutnik Krakow.
Cole is managing an ankle injury, and his withdrawal is thought to be precautionary. Though Cole was clearly unhappy, his movement did not seem to be seriously inhibited.
If Cole has aggravated the injury, Leighton Baines would replace him at left-back for the Sweden game.
Ashley Young, Alex Oxlade-Chamberlain, James Milner and Joleon Lescott also left training early. Martin Kelly was the only absentee from England's training session due to a lingering virus.
Meanwhile England expect a more open game against Sweden in their Euro 2012 Group D test on Friday after the defensive draw against France.
Roy Hodgson's men took the lead in their first game but have been criticised in some quarters for their lack of adventure after France equalised as they sought refuge in the old English trait of being solid but unspectacular.
Danny Welbeck, who started up front alone in the heat of Donetsk and is likely to again in Kiev on Friday, said the Sweden encounter might be more enjoyable for fans given Erik Hamren's men need a result after losing to Ukraine.
"It was quite isolated at times (against the French) but at that level of football you are not going to get so much of the ball," he told a news conference.
"I think looking at it from a neutral perspective, it will be a fun game to watch. It is going to be better for us and once the game gets opened up there will be a few goalscoring opportunities carved out."
Another reason to expect a more attacking display from England is the 19:45 UK time kick off in Kiev compared to the afternoon heat of Donetsk.
"The second and third games in the group are at a later time and it will be a bit better for us," Welbeck added.
Wayne Rooney, suspended until the third group match with co-hosts Ukraine, sported another new haircut in training on Wednesday along with several other members of the squad and backroom staff.
"The barber came in and set up his own barber's shop in Ashley Young's room," Welbeck explained.
Jordan Henderson, a late addition to the squad after injuries to Gareth Barry and Frank Lampard, is England's only recognised spare central midfielder if anything were to happen to captain Steven Gerrard and the terrier-like Scott Parker.
Hodgson hinted after the France game that he may leave one of the duo out against Sweden given they are over 30 and are feeling niggles from a long hard season but Henderson does not expect to start.
He said Gerrard and Parker had done well to combat the French threat while starting numerous attacks of their own and looked fit enough to plough on.
"I think he is getting a lot better. He'll probably be training soon," said Henderson, who like Kelly had an average campaign for a struggling Liverpool side and was a surprise inclusion in the England squad.