Their Nissan Qashqai was travelling along the E4 highway in Stockholm when it careered off an 82ft-high bridge into the Sodertalje canal.
Police divers recovered the bodies of five men – aged between 19 and 32 – from the water. Their names have not been released, but they are understood to be four-piece band Viola Beach.
They were due to play in Guildford, Surrey, on Saturday night, but the venue said the gig had been cancelled due to “unforeseen circumstances”.
Fans have been paying tribute to Viola Beach on social media. Ibiza Rocks tweeted: “Saddened and shocked to hear of the passing of @Viola_Beach. Lovely guys & a band we were big fans of at #RocksHQ”.
The band’s car crashed through a barrier and into the canal after the bridge, at the Saltskogs junction between the E4 and the E20 motorways, opened to let a boat pass underneath, Swedish police said.
The bridge has a middle section that rises upwards, leaving a gap that the car drove into.
Inspector Martin Bergholm said: “For some reason, the car drove through the barriers and crashed down into the canal.”
He added: “The witnesses just saw a car beside them and kind of disappear.”
He said it was not yet known whether the five men were wearing seatbelts but added: “That would not have helped them.”
A Foreign Office spokeswoman said: “We can confirm that five British nationals died in a car accident in Sweden on February 13.
“We are in contact with local authorities and supporting the families at this very difficult time”.