"One cannot, even if there are decades between them, kill millions of Jews so you can bring millions of their worst enemies in their place," he told a French television show.
"I know someone in Germany who took a young Syrian and after four days said, 'The greatest thing Germany invented was the Holocaust,'" he added.
Several hundred people lodged official complaints about Lagerfeld's comments, the French media regulator said Monday after he appeared on the "Salut les terriens!" (Hello Earthlings!) talk show on the C8 channel on Saturday.
The veteran Chanel designer, who was born in Hamburg just as Adolf Hitler came to power, had earlier lambasted Merkel for taking more than one million asylum seekers since the migrant crisis of 2015.
"Merkel had already millions and millions (of immigrants) who are well integrated and who work and all is well... she had no need to take another million to improve her image as the wicked stepmother after the Greek crisis," said Lagerfeld.
"Suddenly we see the pastor's daughter," he said in reference to Merkel's father, who was a Protestant minister in the former East Germany.
Lagerfeld, who is rarely afraid of controversy, said he was going to "say something horrific" before criticising the chancellor for the "huge error" of accepting so many refugees from war-torn Syria and elsewhere.
"Look at France, the land of human rights, which has taken, I don't know, 10,000 or 20,000," he added.
The French TV regulator, the CSA, said it had received several hundred complaints over the weekend about Lagerfeld's comment, and was looking at the programme.
The designer was roasted for the outburst on social media, although some users also came to his defence.