United closed Carrington for the first 24 hours eight days ago and their games at Brentford and at home against Brighton were subsequently canceled.
“Manchester United players have started to re-train at Carrington on a staggered basis,” the club said in a statement.
“The complex was closed for first team operations last week due to a Covid-19 outbreak at the club, but reopened (Tuesday) in the morning.
“So this will now give interim coach Ralf Rangnick and his team time to prepare for our next match – the Premier League meeting with Newcastle United at St James’ Park on Monday 27th December.”
The Premier League announced on Monday that it would continue with its schedule despite widespread coronavirus outbreaks, which forced the postponement of six of the 10 games over the weekend.
The English top flight reported 90 new cases of coronavirus among players and staff last week, a big jump from 42 the previous week.
United are currently sixth in the Premier League table having played two games less than most of the teams above them.
They are due to travel to face Newcastle next Monday, with a home game against Burnley three days later.