It is believed the animal spent about three weeks on the vessel and was finally caught by the crew three days before it docked in Aberdeen.
The North East Wildlife & Animal Rescue Centre (New Arc) charity was called to help by Pest Solutions in the city, who picked up the squirrel from the vessel, Deep Explorer.
New Arc is now caring for the palm squirrel, who has been named Zippy due to his speed, and is said to be doing well after his long voyage ended on Tuesday.
He is faster than a fast thing so he took a bit of effort to catch
Keith Marley, New Arc
Keith Marley, of New Arc, said: “It is a three-week trip from India and the crew got him three days before they got here.
“They looked after him and were feeding him grapes to keep him well after they took him into custody.
“I believe he had been spotted before then but he is faster than a fast thing so he took a bit of effort to catch.”
Zippy has been placed in a large cage at New Arc and is currently being kept in quarantine and monitored.
Mr Marley said: “He is doing well. He was a bit tired and panicked when he first came in, and stressed, but he had a good feed and seems to be behaving very much as a squirrel normally would.”
Palm squirrels, also known as three-striped squirrels, are one of many types of squirrel found in India.
The charity, based in Ellon, Aberdeenshire, is trying to find a permanent home for Zippy.
We've made sure the squirrel is receiving the best possible care. We wish the squirrel well in finding its new home
Deep Explorer Master Maciej Wolinski
Mr Marley said: “In an ideal world we would like to return him home but it’s unlikely we will be able to return him to India.
“We will be checking zoos to see if anyone has this variety of squirrel in their collection in the hope that we can donate him so he can live out his life with his own kind and will hopefully have a comfortable life.”
Master of the Deep Explorer Maciej Wolinski said: “Anyone who’s had a squirrel in their home knows how difficult they can be to capture.
“Our vessel team managed the situation safely and humanely, and we’ve made sure the squirrel is receiving the best possible care.
“We wish the squirrel well in finding its new home.”
Deep Explorer’s owner, oil industry company TechnipFMC, said it could not disclose details of the route its vessel took.