Messi and Barcelona were eliminated at the last-16 stage by PSG following their 1-1 draw on Wednesday evening.
This means that PSG sealed a quarterfinal slot with a 5-2 aggregate victory.
On Tuesday, FC Porto stunned Juventus and Ronaldo after a thrilling extra-time battle in the second leg in Turin.
Messi and Ronaldo to miss quarters
The last time Messi and Ronaldo missed the last eight of the competition was in 2004/2005 season.
Messi and Barcelona were eliminated by Chelsea in the last 16.
Meanwhile, Ronaldo was with Manchester United at the time and they lost in the round of 16 against AC Milan.
Overall, Ronaldo has won the Champions League five times, while Messi has won the competition on four occasions most recently in 2014-15.
With Messi at age 33 and Ronaldo now 36, there has been plenty of speculation that the era of both players dominating the European scene has ended.
This season’s Champions League has seen two players, in particular, emerge as potential successors to the dominating duo.
Kylian Mbappe, whose PSG side defeated Barca, scored four goals over the two-leg tie.
He broke Messi’s record as the youngest player to reach 25 Champions League goals in the process.
Erling Haaland also scored four goals in Dortmund’s last-16 tie against Sevilla.
The 20-year-old striker became the youngest player to reach 20 Champions League goals.