"This was first and foremost a crime against this insurance agency", Ravi Landolt, a senior investigator for regional police in Schaffhausen said.
Police described Wrousis as a 6-foot-2 loner with an unkempt appearance who mainly lives in forests but who visits populated areas.
The attack happened inside an office building on a shopping street in the centre of Schaffhausen, a medieval town of 36,000 inhabitants on the German border, police said.
The 50-year-old suspect remains on the run a day after the attack on Monday.
Police also published several photos of the man, the latest of which they said was taken shortly before his attack on the CSS insurance office. In a statement, they said they do not even have a rough idea where he is, and admitted that he may have fled the country. He is still believed to be in possession of the chainsaw and was booked for two weapons-related offences in 2014 and 2016.
Swiss police detained Franz Wrousis in Thalwil, about 40 miles (64km) from Schaffhausen where the incident in which two people were injured, took place.
Insurer CSS spokeswoman Christina Wettstein told Blick the two were undergoing medical operations after the Monday morning attack and she doesn't know how they are doing.
Police released photos of the suspect, showing a man standing in the woods with slumped shoulders. They did not elaborate on its condition or say if anything else was found in it.
"We are searching for a man whose description is now known".
Police said the suspect was likely driving a small white van with Swiss number plates.
A local official in Zurich canton, Ruedi Karrer, told the 20Minuten website he had seen Wrousis in the Uhwiesen forest while walking his dog and believed the suspect had been staying there for about two weeks.
"He may have been a little unusual, but he wasn't unfriendly", she said.