Mourinho hit back at remarks by Barcelona coach's Tito Vilanova last weekend that Messi, who has won the award for the past three years, was "the best [player] in the world by a long way".
"When someone with the same responsibility as me comes out and says: 'Mine is the best on the planet' then I have to say: mine was not born in Madeira, he was born on Mars; he is not from planet Earth, he is the best in the universe," Mourinho told Portuguese daily A Bola in an interview.
"If Messi is the best on the planet, Ronaldo is the best in the universe. It would be a crime if Ronaldo did not win the Ballon d'Or."
Ronaldo won the award in 2008 and Mourinho said it was time to recognise him again.
"If you are going to give out the Ballon d'Or because a player is the best, give it to Cristiano or Messi. But I ask: if the two are on the same level, is it normal that one wins four and the other one? It is not."
In Sunday's 2-2 La Liga draw at the Camp Nou, Ronaldo became the first player to score in six consecutive 'Clasicos' with his ninth and 10th strikes on his 16th appearance against Barca.
Mourinho said a player needed to win big titles to deserve the Ballon d'Or.
"How can you win the Ballon d'Or without collecting titles, without winning anything important? Don't come to me telling me about the Intercontinental Cup or the Supercup, this is small stuff. Tell me about fat titles," Mourinho said.
The Portuguese coach said Ronaldo had had a tougher career than his Argentine rival.
"It is harder to be Cristiano than Messi. Messi grew up in the team where he plays, with the players with whom he plays. Not Cristiano. He was in England, then they put him here in a losing team. He had to grow over the last two years with this team which has been forming," Mourinho said.
"One [Messi] plays as a [number] 9 and roams around in those 50 square metres where the distance to goal is smaller and defence less intense.
"The other [Ronaldo] plays as a winger. How does a winger score as many goals as a number 9? Besides, Ronaldo is a player who is not protected by anyone."
The Ballon d'Or, which merged with the World Player of the Year award in 2010, will be awarded on January 7 in Zurich.
