The 44-year-old Portuguese soccer boss was held late on Tuesday after an animal health official and two police officers went to his central London home to remove his dog, the Sun newspaper reported.
The paper said the official wanted to put the dog into quarantine, believing it had been taken out of Britain and then brought back without the necessary inoculations.
It said Mourinho refused to let the official take the dog and was arrested at around 10 p.m. after arguing with police.
The Sun said Mourinho had been at Chelsea's player of the year awards and rushed home when he was called by his wife Tami.
Police left without recovering the dog, which the Sun said was now on the loose.
A Scotland Yard spokesman said: "A 44-year-old man was arrested on suspicion of obstructing police. He subsequently received a caution for obstructing police."
He said an officer from the Animal Health and Welfare Service had gone with police officers to seize the dog because of alleged offences under the 1981 Animal Health Act and the 1974 Rabies Order.
He confirmed the animal had not been recovered.
Mourinho's team play Manchester United in the FA Cup final at the new Wembley Stadium on Saturday.
