The incident happened in the popular Botchergate area, which is full of bars and pubs and a weekend hotspot.
It was witnessed by dozens of revellers from Dumfriesshire, with many taking to social media to express their shock.
The crash, at about 7 pm, involved two cars, but Cumbria Police say they don’t believe it was a deliberate act.
A spokesman for Cumbria Police said: “Police are currently dealing with a road traffic collision on Botchergate, outside the Rambler pub.
“The incident occurred around 7 pm and involved a taxi, a black Ford Fiesta and three pedestrians.
“This is not being investigated as a deliberate act. Injuries are not believed to be life threatening.
“All parties involved are currently being supported by emergency services and the police are not looking for anyone else in connection to this incident.
“The Botchergate road has been closed earlier than normal to vehicles to allow emergency services to attend the scene and recover the vehicles.”
