"New Zealand Police can confirm an allegation is under investigation, reported to us on 10 April 2026 in central Auckland," police said in a statement without giving further details.
The New Zealand Herald newspaper reported a player was being investigated over an alleged sexual assault at the team's hotel after Cape Verde's March 27 match against Chile in Auckland.
Cape Verde's soccer federation was not reachable for comment on Monday.
A spokesperson for FIFA said the sport's global governing body was not in a position to comment as it was an ongoing investigation.
New Zealand Football, the host federation for the FIFA Series matches in the nation, said they had not been contacted by police about the matter but would assist with any enquiries if required.
Cape Verde, an archipelago off the coast of West Africa, will make their World Cup debut at the June 11 to July 19 tournament co-hosted by the United States, Canada and Mexico.
The team play former champions Spain and Uruguay, and Saudi Arabia in the group phase.