The Marmoset monkey will be taken to Monkey World rescue centre in Dorset some time next week, according to reports by the BBC.
According to the BBC, police officers stopped the vehicle that was travelling on the M6 at around 6.30pm on April 8.
Two people have been arrested.
In a statement Cumbria Police told the BBC: “The driver, a man, was arrested on suspicion of driving a vehicle in a dangerous condition and drug driving.
“The passenger was arrested on suspicion of illegal possession of a primate after the discovery of a Marmoset monkey in the vehicle’s boot.”
During an interview with the BBC, Monkey World director Alison Cronin got a phone call about the rescue.
“We are going to make it a priority to give it a pair of parents to look after it for the rest of its life” she said.
“I don’t even know what to say. It’s still happening today. The laws have now changed. People have to be licensed properly.”