The 34-year-old man, identified as an Iraqi national, "was critically injured in a shootout with police officers as he left the disco, and later succumbed to his wounds in hospital," police said in a statement.
"We're not assuming that this is an act of terrorist violence," police spokesman Fritz Bezikofer told rolling news channel NTV.
"The events in the disco and all the links are somewhat clearer and they actually rule out a terror background," he said, adding that the gunman was not an asylum seeker and has been living in Germany for some time.
Another police source said he could have been motivated by personal relationship issues.
Officers began receiving emergency calls from terrified clubbers at around 4:30 am (0230 GMT) as the man began shooting in the nightclub heaving with "several hundred" people, said police.
One person was killed on the spot and three others seriously wounded in the club called "Grey", located in an industrial zone in Constance, a city on the banks of the eponymous lake near the Swiss border.
Shortly after the gunman left the building, he was shot by police. One officer was also injured in the exchange of fire.
Terrified nightclubbers had either fled the building or found a place to hide, police said, adding that the danger was now over.
Helicopters were circling overhead and special forces were also deployed to secure the site.
'Club was jam-packed'
A witness told national news agency DPA that the attacker was shooting randomly at clubbers around him.
A bouncer at the site had sought to stop the attacker, but was himself injured by the man, local broadcaster SWR said, also reporting witnesses saying that the gunman was armed with an automatic pistol.
Police was unable to confirm the type of weapon used, but Bezikofer said it was "not just a pistol, the talk is of a long weapon or an automatic pistol".
The shooting came just two days after Germany was shaken by a knife attack in the northern port city of Hamburg.
A 26-year-old Palestinian had killed one and injured six in an assault at a supermarket.
He was a known Islamist with psychological problems, and investigators say his motives remain unclear.
Germany has been on high alert about the threat of a jihadist attack, especially since last December's truck rampage through a Berlin Christmas market that claimed 12 lives.
But it has also been hit by other assaults unrelated to the jihadist threat.
Among the deadliest in recent years is a Munich shopping mall rampage by 18-year-old German-Iranian man which left 10 people dead including the gunman himself.
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)
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