"We condemn this senseless act and believe the police will find the perpetrator as soon as possible. We hope the honorary consul will recover soon," said spokeswoman Danijela Barisic.
She added that Foreign Minister Vesna Pusic had spoken with Dutch Ambassador Stella Ronner-Grubacic and Interior Minister Ranko Ostojic about the case.
The 72-year-old consul, Silvana Kondic, was attacked with a knife to the head and neck in her office in downtown Split and was taken to hospital, police said.
She received "several stitches" and is not in danger, the Split Hospital said.
According to unofficial information, the arrested man has dual Croatian and Dutch citizenship.
Police are investigating the case.
The Dutch Consulate in Zagreb said it would release a statement later in the day.
Kondic was visited in hospital by Split Deputy Mayor Aida Batarelo, who told reporters Kondic was in shock and that the man who attacked her was probably a drug addict and that he had asked her for money several times before.