On Monday, Merkel's spokesman said that Gauland's quote was "a vile and a sad sentence."
Vice Chancellor Sigmar Gabriel said that it was wrong to describe the issue as xenophobia.
"Boateng is a German," Gabriel tweeted. "The AfD is anti-German."
Merkel's spokesman Steffen Seibert condemned the statement on Monday, after numerous German politicians, football fans, and activists accused Gauland of racism toward the national team member.
The outrage started when Gauland, the deputy head of Alternative for Germany (AfD) party, mentioned Boateng in an interview with Frankfurter Allgemeine Zeitung.
"People find him good as a footballer. But they don't want to have a Boateng as their neighbor," he said for the paper's Sunday edition.
Boateng was born in Berlin to a German mother and a Ghanaian father.
Head of the ruling CSU party, Horst Seehofer, said that Gauland had "completely disqualified himself" as a politician.
"The way he is presenting himself is embarrassing. I actually thought that something like that was not possible in Germany anymore," the Bavarian conservative said.
Right-wing party blames paper
The right-wing AfD seemed to distance itself from the statement, with Gauland himself claiming he was talking hypothetically about other people's views. Earlier, Gauland stated he had no intention of attacking Boateng personally.
"Of course I am not a racist," he told the German DPA agency on Monday. At the same time, Gauland added that some people responded "with an almost instinctive defense" to foreigners in their environment.
When asked if people who were reserved about foreign neighbors were racist, he said: "I wouldn't go that far."
According to an AfD spokesman, the party now considers filing an injunction against Frankfurter Allgemeine Zeitung, blaming the paper for allegedly misinterpreting Gauland's words. The newspaper had titled their article "Gauland insults Boateng."
AfD party chief Frauke Petry, who is also Gauland's direct supervisor, sought to limit the damage on social media.
"Jerome Boateng is a quality player and deservedly part of the German national team," Petry wrote on Twitter.
She also "apologized" to Boateng for the impression created by Gauland, according to the wide-circulation Bild newspaper.
'Proud' to be German
German national team members expressed their solidarity with Boateng in a short video titled "We are diversity."
"Honestly, it's said that things like that are still being said today," Boateng said after the friendly with Slovakia on Sunday.
"I am happy to be German, I am proud of it, or I wouldn't be here in the team. I think I am well integrated, and I don't need to say any more about it."
During the game, many German fans carried banners saying "Jerome, be our neighbor," or "Please move in next door."