Promes missed training with Ajax on Sunday following his arrest and is denying any involvement in the alleged incident.
Promes' lawyer told Dutch news agency ANP: "Promes was not on site at the time of the incident. Promes is fully cooperating with the investigation."
Dutch newspaper De Telegraaf reported a stabbing happened in Abcoude, just south of Amsterdam, at a family reunion hosted by Promes on the premises of a company he owns. The report added the player got into a fight with one of his relatives there and stabbed him.
"It's very worrisome but being accused of something doesn't mean you did it," Ajax had told FOX Sports Netherlands in a statement following his arrest. "It is therefore too premature to say anything about it from Ajax."
Police did not confirm the identity of the suspect but said a 28-year-old from Amsterdam had been arrested in connection with the alleged incident. Police said the man stabbed, who was seriously injured in the incident, pressed charges last month.
Promes has scored seven goals in 47 international appearances for the Dutch national team, and scored Ajax's second goal in their 4-0 win over PEC Zwolle on Saturday.
Ajax face Utrecht in the Dutch Cup on Wednesday with Promes in contention to make the squad.