Customers in the bar were watching football on television when at least two gunmen, reportedly wearing skeleton masks, launched their shooting spree.
"We are assuming that this is gang-related and not a terrorist attack," police spokesman Björ Blixter told the AFP news agency.
"We've had similar problems with shootings for several years but never of this magnitude."
A manhunt has been launched for the gunmen who fled by car after the shooting in a heavily immigrant area of Sweden's second city.
Blixter said two people died and between 10 and 15 were wounded, but the death toll could rise.
Sahlgrenska University Hospital said it was treating eight patients from the shooting, including one with life-threatening injuries and two in serious but stable condition.
Gothenburg police said they have launched a murder investigation and are questioning a large number of people but no arrests have been made.
Sweden and neighbouring Denmark have a longstanding problem with criminal gangs, including Hells Angels, Bandidos and several immigrant groups which battle for control of the local drug trade.
The shooting fitted a pattern of regular tit-for-tat retributions between rival gangs in areas with high immigrant populations in Gothenburg, which lies on Sweden's southwestern coast and has a population of 550,000.
One witness told the Aftonbladet tabloid that two people entered the pub in Gothenburg's heavily immigrant suburb of Biskopsgaarden armed with weapons that looked like Kalashnikovs and started shooting.
Another witness said the shootings were over quickly.
"I didn't have time to think what was happening. Then I saw that my friend was bleeding. I tried to stop the flow of blood as well as I could with my hands," a man who gave his name as "Rocky" told public broadcaster SVT.
The bar is located on a small square next to a grocery shop and several tobacco kiosks.
There have been dozens of gang-related shootings in Gothenburg in recent years, many of them in the Biskopsgaarden area, a housing estate with a large immigrant population and high unemployment, but fatalities are relatively rare.
According to local tabloid GP, there were a total of 52 shootings in Gothenburg last year, of which four were fatal.
In 2010, Biskopsgaarden became one of the first areas in Sweden to mount video surveillance cameras in public places because of the high level of crime in the neighbourhood of 12,000 people, according to the municipality.
In some areas of Biskopsgaarden, 80 percent of inhabitants are of immigrant origin.
A man was shot dead in an apartment in the area in May last year and two others died in suspected gang-related shootings during an upsurge in violence in late 2013.
In January a man was shot in the leg close to the scene of Wednesday's shooting.
"It's frightening. Things happen nearly every day here but this looks like something extra," one local resident who did not give her name told Aftonbladet.
However another resident said the area around the pub was usually quiet.
"This is actually a quiet area… there have been occasional shootings but never anything serious. It's all between gangs," she said.
Sweden is as a whole a tranquil country of 9.5 million people, and gun-related deaths are uncommon.
In 2013, a total of 87 violent deaths were reported in the country. Of those 26 were gunshot fatalities, according to the Swedish National Council for Crime Prevention.