The 21-year-old, who spent last season on loan at Everton from Chelsea, came on after 61 minutes of Belgium's 1-0 friendly victory against Tunisia in Brussels but limped off shortly before the end of the match.
"He's in pain but the doctors don't think it's too serious, at least at first glance," said Wilmots.
"He will be checked over more closely on Sunday but it's probably a bad sprain. Hopefully he just needs three or four days to recover."
The news of Lukaku's injury was a worrying development for Belgium, who lost Aston Villa striker Christian Benteke to a ruptured Achilles tendon in April.
Teenage Lille player Divock Origi, who started on Saturday before being replaced by Lukaku, is the only other specialist striker in the squad, although Wilmots can call on an enviable cast of attacking talent including Premier League stars Adnan Januzaj, Eden Hazard and Kevin Mirallas.
Wilmots criticised Tunisia for what he perceived as an overly physical approach in a friendly game so close to the start of the World Cup.
"I had hoped there wouldn't be any injuries but in the changing rooms all I saw were bruises and ice-packs," he said.
Belgium are in Group B in Brazil, kicking off their campaign against Algeria on June 17 before taking on Russia and South Korea.