The 33-year-old defender was named in Argentina's squad for a friendly against Ecuador this month, but Inter insist the former Napoli man is injured.
Campagnaro has not played for Inter since their victory over Fiorentina on September 26, but did feature in his country's FIFA World Cup qualifying defeat against Uruguay last month.
Sabella claimed Campagnaro informed him he is not carrying an injury, but the Italian club are adamant that is not the case.
A statement on Inter's official website said: "After returning from international duty, the player suffered a rectus femoris injury in his right thigh while training on the Saturday before Inter's away game at Torino on 20/10/13.
"Following this new injury, the player began his rehabilitation and missed the next three games: Inter v Verona on 26/10/13, Atalanta v Inter on 29/10/13 and Udinese v Inter on 3/11/13.
"The player has not yet trained again with the rest of the team but has only done rehabilitative training with a fitness coach. He has not been available to the coach for selection.
"All this information was made available to the Argentina medical staff before Campagnaro's most recent call-up.
"FC Internazionale does not accept having the professional honesty of its technical and medical staff called into question.
"FC Internazionale wishes to express its surprise at having been ignored by the Argentine Football Federation whenever attempts at direct contact have been made during the above-mentioned period.
"Furthermore, FC Internazionale stresses its disappointment at the statements attributed to Mr Sabella, considering the large number of Argentine players at the club and the long-standing, friendly and respectful relationship with the AFA and its representatives, with whom Inter has always collaborated with mutual satisfaction."
