The quandary arises because both the father, Arnor Gudjohnsen, 35, and his son Eidur-Smari, 17, played in Iceland's 3-0 friendly win over Estonia in Tallinn, but Eidur-Smari came on as a 62nd-minute substitute for his father.
Ray Spiller, of the British-based Association of Football Statisticians, said: "We're not sure how to clarify this one. They played in the same team but not together, so in a sense they made history and in another they didn't. I just hope they play in the same team at the same time in Iceland's next match."
A spokeswoman for the Icelandic FA said: "Arnor gave his son a hug and a kiss and wished him good luck when he replaced him. They thought it was fine, but the media were not too happy."