Swansea City are investigating allegations a club director made disparaging comments about Manchester United manager Louis van Gaal.
"It is disappointing that one of our directors has apparently made a statement in the media in relation to a manager of another club," Swansea chairman Huw Jenkins said.
Van Zweden joined the board in 2002.
Jenkins added: "Our football club prides itself on having a good working relationship with all Premier League clubs, managers and staff.
"We feel we have built up that good relationship over a number of years and will continue to work hard to preserve our image within the Premier League and the game in general at all costs.
"If any of our directors behave in an inappropriate and unprofessional manner not befitting this football club then they will be dealt with internally and appropriately.''
Van Gaal and Van Zweden are both Dutch, with the United manager coming from Amsterdam and the Swansea director from Den Haag.
Van Zweden taunted United's Dutch players Daley Blind and Robin van Persie after the game, tweeting: "Great. First The double over #louisvangaal #vanpersie and @BlindDaley and also another @ADODenHaag win. What a beautiful da!"