South Wales Police said they attended the Tesco store on Western Avenue just after 14:00 BST after Avon and Somerset Police asked them to stop a vehicle.
A spokeswoman said armed officers were deployed "as a precaution" and part of the store's car park was closed while arrests were made.
She said two men were arrested on suspicion of money laundering and no firearms were recovered.
The spokeswoman added that "there is no suggestion it is terrorist related".
Eyewitness Sean Martin, 31, from Cardiff, said the police were waiting for the men as they drove out of the car wash.
"They were all pointing their guns at the car," he said.
Armed officers arrested two men at a Cardiff supermarket on Saturday.