The 25-year-old man and the 23-year-old woman had decided to take a shower together on Saturday evening, the Aftonbladet newspaper reported.
Friends staying in the next room rushed in to the couple's room after hearing a scream.
"One of the friends ran in, but found both of them dead. When she tried to revive her friend, she received an electric shock," a family friend told the newspaper.
The Swedish foreign ministry has confirmed the deaths.
According to a representative with the Swedish embassy in Bangkok, one theory the police are investigating is that the hotel room shower somehow became electrified.
The four Swedish travellers, all of whom come from a small village in Jämtland County in northwestern Sweden, were at the start of what was to be a month-long trek throughout Asia.
Following the accident, however, the second couple has decided to come back to Sweden.
According to Aftonbladet, the accident isn't the first time that Swedish tourists have been killed in Thailand by an electrified shower.
In 2007, a 34-year-old man from the Stockholm area died after being electrocuted in his hotel shower in a resort in Patong.