The Portuguese international was flabbergasted that his La Liga rivals had spent £97million on the Borussia Dortmund winger.
Dembele penned a five-year contract at the Nou Camp and has a £367m buy-out clause.
He became the second most expensive player in the world, behind Neymar who moved to Paris Saint-Germain for £200m.
But his life at the Catalan club got off to a nightmare start as he suffered a season-ending injury just three games in.
It is reported Ronaldo responded by saying “who is that?” when he first heard Dembele moved to Barcelona.
He then went on to insult the France international further, according to Spanish publication Diario Gol.
Ronaldo apparently said that he was only at Dortmund to play with highly-rated striker Pierre-Emerick Aubameyang.
He then claimed that his move to the Nou camp solely to partner Lionel Messi.
Ronaldo said: “(He) comes to Barca with the mission to play for Messi, like everyone else.”
However, the 32-year-old should know who Dembele was having faced him twice in the Champions League last season.
Both games ended in 2-2 draws in the group stages.
Ronaldo has come under criticism this season as Real struggled to defend their La Liga title.
Zinedine Zidane’s side are 10 points behind league-leaders Barcelona.