The final result at Allianz Arena saw Hansi Flick's side progress to the quarter-finals of the competition 7-1 on aggregate, with a heavyweight encounter against Barcelona up next.
The Blaugrana beat Napoli 3-1 to book their place in the last eight, with Messi grabbing the headlines for a stunning solo goal which saw him take on five defenders and pick himself up from the ground before curling the ball into the far corner of the net.
The diminutive Argentine is widely considered to be the greatest footballer in history, and he picked up a record-breaking sixth Ballon d'Or award in 2019 after another stellar year.
Messi has carried a disjointed Barca side once again over the course of the current campaign, but Matthaus believes Lewandowski has now overtaken the 33-year-old as the best in the business.
Ahead of Bayern's clash with the Spanish outfit in Lisbon on Friday, the club legend told Bild: "Messi faces his successor as the best player in the world: Robert Lewandowski. He is the best player, not just the best forward.
"The Barca of today is no longer the same as before. They have Messi, of course. A player like him is always capable of genius.
"But he alone will not be enough against this Bayern. Barcelona does not scare me."
Matthaus is confident that his old club will reach the Champions League semi-finals at Barca's expense, as he told Sky Germany: "Naturally Barcelona have enough quality to produce the best of themselves in one game, but I think Bayern will have to make many mistakes and do many things wrong to lose against this Barcelona."
Bayern striker Thomas Muller was asked to weigh in on the Lewandowski-Messi debate after their victory against Chelsea, and urged his team-mate to prove that he deserves to be mentioned in the same breath as the Barca talisman.
"We'll see that on Friday. Lewy will have to answer this question," said the Germany international.
"Messi also played very well [against Napoli]. But it's up to Lewy and us to answer this question in Lewy's favour on Friday."