As Britain prepares to vote on hopping out of the EU on Saturday, Mr Baker, who is chairman of the pro-Brexit European Research Group, tweeted video of a lost and lonely looking marsupial.
The Conservative member for Wycombe said: "It's been a strange day."
Asked on Twitter if he had suddenly flown to Australia, Mr Baker replied “It’s a loose one in Bucks.”
Another reply said: “Perhaps it’s hopping mad at Boris Johnson’s (Brexit) deal.”
Mr Baker’s fellow Tory, Cllr Gary Stevens asked “Has Skippy come to the rescue, Steve? Is the Commonwealth trying to say something, Skip?”
The assumption the loose marsupial was a kangaroo might have been incorrect, however, with one keen-eyed respondent tweeting “Alright, calm down, it’s only a Wycombe Wandering Wallaby.”
If so, it would not be the first time a wallaby has been at large in the area.
A wallaby was killed when hit by a car on the M1 in August 2005.
The driver, Rev Stephen Trott, of Boughton, Northants, reported to Thames Valley Police that he had hit a kangaroo, before it was confirmed the animal was a wallaby.
At the time, a spokeswoman for nearby Woburn Safari Park said none of its wallabies were missing but there were pockets of wild wallabies living in the region.
“They have been established a long time after escaping from various parks a long time ago,” she said.
“It is quite unusual for them to be near motorways with all those cars streaming past because they are generally very shy animals.”
There have been sporadic sightings of kangaroos and wallabies in Britain over the years.
There was a colony of red-necked-wallabies in the Peak District in the 1950s and early 1960s whose population reached around 50.
Many of them died during the severe winter of 1962-1963, and they are thought to have died out in the late 1990s.
Thames Valley Police officers said they had no reports of a missing kangaroo or wallaby on Friday, but with England playing the Australian Wallabies in the Rugby World Cup quarter-final on Saturday, perhaps the rogue marsupial was sending a message.