Kushner, who is Jewish and whose son is married to US President Donald Trump's daughter, published the open letter in the Wall Street Journal amid deep divides between France and the US and Israel.
In the letter, he urged French President Emmanuel Macron to more urgently enforce hate-crime laws and tone down criticism of Israel, saying French government statements about recognising a Palestinian state have fuelled anti-semitic incidents in France.
"France has learned of the allegations made by the United States Ambassador, Mr Charles Kushner, who, in a letter to the President of the Republic, expressed his concern about the rise in anti-semitic acts in France and noted the alleged lack of sufficient action by the French authorities to combat them," the ministry said.
"The ambassador's allegations are unacceptable," the ministry said, adding Kushner would be due to appear on Monday.
Kushner's letter follows another sent to Macron by Israeli Prime Minister Benjamin Netanyahu earlier this week in which Netanyahu accused Macron of contributing to anti-semitism by calling for international recognition of a Palestinian state, according to the Jerusalem Post.
Macron has emerged as one of the more forceful critics of Netanyahu's prosecution of the war in Gaza, particularly with regard to Palestinian civilian casualties, while Trump has steadfastly supported the Israeli leader.
"Public statements haranguing Israel and gestures toward recognition of a Palestinian state embolden extremists, fuel violence, and endanger Jewish life in France. In today's world, anti-Zionism is anti-semitism - plain and simple," Kushner wrote.
Kushner's son Jared Kushner is married to Trump's daughter Ivanka Trump, who converted to Judaism before their wedding in 2009. They have three children who are being raised Jewish.
Macron has publicly criticised anti-semitism as antithetical to French values and increased security to protect synagogues and other Jewish centres in response to anti-semitic incidents linked to the Gaza conflict.
