The Manchester City midfielder started all three of England’s group-stage matches in Germany as Gareth Southgate’s side advanced by finishing top of Group C.
But the FA said in a brief statement on Wednesday that Foden would leave the team’s GolfResort Weimarer Land base near Erfurt for a spell.
No information has yet been provided about when the player might return.
Sky Sports News senior reporter Rob Dorsett, who is in Germany with the England squad, said: “It is well known that Foden is having a third baby with his girlfriend Rebecca Cooke. They confirmed that in April with a baby shower in Stockport and they put some photos on his Instagram account announcing the happy news.
“So, my understanding is that Foden wants to go back and be with his girlfriend for a very short period of time before he comes back out to Germany to continue with England and this tournament.”
England will discover their last-16 fate on Wednesday evening, with either the Netherlands or the third-placed team in Group E their first knock-out opponents in Gelsenkirchen on Sunday (5pm kick-off, UK time).