The man, identified as C.R., was implicated in an incident that occurred last Thursday at an army checkpoint in the province of Nigde, the English-language version of the Hürriyet newspaper reported online.
He was with two alleged accomplices, a German-Chinese and a Macedonian in a pickup truck, Swiss media said.
“I did a good deed by killing the Turkish gendarmerie soldier,” the Swiss man, originally from Kosovo, told police, the Dogan News Agency said.
A soldier and a policeman were killed in the attack, the agency said.
“I don’t render an account to anyone but Allah,” the Swiss suspect said.
“I will not give any testimony — you are all pagans,” he was quoted as saying.
He reportedly said that Turkey was considered an enemy for being a Nato member.
The assailants, who were captured within hours, are suspected of being members of a jihadist group linked with al-Qaeda known as the Islamic State of Iraq and the Levant, Hürriyet said.
The driver of the pickup truck denied being part of the attack and explained he was accompanying the Swiss man, whom he did not know, back to Kosovo, the newspaper said.
The driver, apparently German-Chinese, reportedly said he was under the influence of drugs and did not see if any police or soldiers were shot.
“When (C.R) saw the checkpoint, he directed his gun behind my back and started to open fire,” the driver is quoted as saying.
“When I asked him what happened, he shouted at me, telling me to drive the truck.”
The Swiss foreign affairs departments said it was aware of the press reports of the case and was in the process of seeking further information.
Turkish Prime Minister Recep Tayyip Erdogan last week condemned the shootings as a "nefarious terrorist attack".
It is not clear what the motive of the attack was, although a government minister has indicated there may be Syrian links.
The shootings came as the Turkish prime minister became embroiled in controversy over banning Twitter before crucial local elections.
Erdogan justified the ban by stating that the social media site runs "all kinds of lies".
Critics condemned the move calling it a bid to muzzle a widening corruption scandal dogging the government, AFP reported.