The Dutch champions issued an advert in a national newspaper requesting information regarding his whereabouts as they claim the Dane owes them £2.5million for unpaid tax bills.
Laudrup was forced to cancel his trip to Holland to watch Swansea's youth team and his attendance of Swansea's pre-season fixture against Eredivisie side Excelsior Maassluis has also been put in jeopardy.
Ajax want the 48-year old to appear in front of magistrates to settle the dispute but Swansea director John van Zweden believes they have been unprofessional in dealing with the case.
"I have spoken to Michael at length about his tax issue. He is shocked. Ajax have portrayed him as a criminal, as a tramp without a proper address or place to live," he said.
"They have advertised they don't know where Michael Laudrup is and therefore summoned him via a legal advert to appear in court within two months.
"We are taking about the manager of Swansea City. Ajax make out this is a criminal who is hiding and sleeping under bridges next to a river.
"The entire world knows where Michael Laudrup is. Everyone knows he is the manager of Swansea City."
However, an Ajax spokesman defended themselves, saying that taking out a newspaper advert was the necessary action to take.
"This is the formal procedure for legal action when the person involved is not living in the Netherlands or does not have a permanent address abroad," the spokesman said.
"It is a big debate about gross and net wages, which were paid to Laudrup. We can do nothing else but ask the players from that time to pay us the money back which they should have paid to the tax man."