Osimhen did not fly with the squad from Abidjan, where they beat Angola in the quarterfinals on Friday.
"Team medics confirmed that he has been placed under close watch with a member of the medical team staying behind in Abidjan with him. If cleared by tomorrow morning, he will join the rest of the squad before 5 p.m," a Nigerian Football Federation statement said.
Nigeria plays next on Wednesday against South Africa in semifinals of the 2023 Africa Cup of Nations, a match that will be held in Bouake.
Osimhen's absence would be a major blow to Nigeria, for whom he has been their outstanding performer at the tournament with his endless running and phenomenal work rate.
The Bouake clash is followed on Wednesday by the second semi-final in Abidjan where the hosts Ivory Coast face Democratic Republic of Congo.