Ronaldo played 90 minutes for Real Madrid in their 3-0 derby win over Atletico in the first leg of the sides' Copa del Rey semi-final on Wednesday.
It was an eventful birthday for the Madeira-born forward, who turned 29 on Wednesday, as he was also hit with a three-game ban by the Spanish Football Federation (RFEF) earlier in the day for his red card and subsequent gesture to the officials in Madrid's 1-1 draw at Athletic Bilbao on Sunday.
The 2013 Ballon d'Or winner was also inundated with congratulations from fans on Twitter, but is unlikely to have expected a message from Ibrahimovic.
"Happy birthday @Cristiano!" the Swede wrote. "I have sent your new favourite outfit in the post."
The tweet included the hashtag #DareTo Zlatan and a picture of a T-shirt bearing the same slogan.
And later on Wednesday, Ronaldo replied: "Thank you for the birthday present, @Ibra_official. It will look better on me than you though."
Thank you for the birthday present @Ibra_official. It will look better on me than you though.— Cristiano Ronaldo (@Cristiano) February 5, 2014
The two players maintain a healthy rivalry and went head to head for a place in this year's World Cup in a play-off back in November.
Before those fixtures, Ibrahimovic claimed he was the better player, but Ronaldo had the last laugh as he hit four goals in the two games to secure a World Cup spot for Portugal at the expense of the Swedes and their mercurial striker.