By Agence France-Presse
The assailant has been identified as Franz Wrousis, 51, who has a criminal history and had reportedly been living in a forest.
Wrousis targeted the CSS insurance company on Monday in the northern town of Schaffhausen, storming into their office where he injured two people, one of them seriously.
Three other people suffered various injuries amid the fracas but none of the victims are currently in critical condition, public broadcaster RTS reported.
Wrousis fled the scene and was caught on camera carrying a black bag and a rucksack that likely contain the chainsaw and possibly other weapons, the 20Minuten website said, quoting Schaffhausen police.
An international arrest warrant has been issued for Wrousis, local media said, citing police.
Although Schaffhausen is near the German border, there is no evidence indicating the suspect has left Switzerland, RTS reported.
According to 20Minuten, the areas along the Swiss-German border were being scoured with the help of sniffer dogs but the assailant's whereabouts remain unknown.
Police have distributed multiple photos of Wrousis, including one of him looking dishevelled in a forested area.
On Tuesday they released a second image captured by a surveillance camera in which he is seen with his hair trimmed and wearing a green coat.
Police have said that roughly 100 officers are involved in the manhunt, including German officers.
The chief of security in Schaffhausen, Ravi Landoldt, has described Wrousis as a "dangerous and aggressive man," who had been convicted for weapons offences in 2014 and again in 2016.
A local official in Zurich canton, Ruedi Karrer, told 20Minuten he had seen Wrousis in the Uhwiesen forest while walking his dog and believed the suspect had been staying there for about two weeks.
Several other residents told the site they had also passed by Wrousis in the forest -- about two kilometres from Schaffhausen -- and that his behaviour had been threatening.