The forward, who had already scored a glorious goal from long-range, was denied by Keylor Navas, the home goalkeeper deflecting his spot-kick onto the crossbar.
Messi had scored a penalty for Barca in the first leg of the last-16 tie against PSG, which the French champions won 4-1 at Camp Nou.
The last time Messi failed from 12 yards was against Valencia in December, although the ball was ultimately recycled so that he headed home in the aftermath.
Long-time rival Cristiano Ronaldo fared little better in that same December week.
Despite his confident-as-ever run-up, his weak effort was saved by goalkeeper Pierluigi Gollini.
That was Ronaldo's third penalty miss of 2020, having previously failed to convert spot kicks against Sampdoria in Serie A in July and versus Milan in the Coppa Italia semi-final back in June.
Ronaldo, though, did score his last penalty in the Coppa Italia against Inter on February 2. He has netted seven and missed one of his attempts this season.
Looking back over the last five seasons in all competitions, Ronaldo has missed nine penalties in total but scored 48.
Ronaldo penalties missed - last five seasons
|Juventus||20/21||Serie A||Juventus 1-1 Atalanta|
|Juventus||19/20||Serie A||Juventus 2-0 Sampdoria|
|Juventus||19/20||Coppa Italia||Juventus 0-0 Milan|
|Juventus||18/19||Serie A||Juventus 3-0 Verona|
|Portugal||17/18||World Cup 2018||Iran 1-1 Portugal|
|Real Madrid||17/18||La Liga||Real Madrid 3-2 Malaga|
|Real Madrid||16/17||La Liga||Real Madrid 2-1 Valencia|
|Portugal||16/17||WCQ||Portugal 4-1 Latvia|
|Real Madrid||16/17||La Liga||Alaves 1-4 Real Madrid|
Over the last five seasons in all competitions, Messi has missed nine penalties, and scored 33. His record this season is 8-2 from 10 attempts.
Messi penalties missed - last five seasons
|Barcelona||20/21||Champions League||PSG 1-1 Barcelona|
|Barcelona||20/21||La Liga||Barcelona 2-2 Valencia|
|Argentina||19/20||Friendly||Brazil 0-1 Argentine|
|Barcelona||18/19||La Liga||Barcelona 1-0 Real Valladolid|
|Argentina||17/18||World Cup 2018||Argentina 1-1 Iceland|
|Barcelona||17/18||Copa del Rey||Espanyol 1-0 Barcelona|
|Barcelona||17/18||La Liga||Barcelona 4-0 Deportivo|
|Barcelona||17/18||La Liga||Alaves 0-2 Barcelona|
|Barcelona||16/17||La Liga||Barcelona 4-2 Eibar|
The miss for Messi against PSG was the first time either he or Ronaldo had missed a penalty in the calendar year 2021.
Ronaldo has taken and converted more penalties than Messi in the last five years, as well as having a better success rate.
Messi v Ronaldo - Penalties
|Player||Penalties taken||Penalties Scored||Conversion Rate|