Bezalel Smotrich, a member of the nationalist right-wing Jewish Home party, made the comments on Twitter on Tuesday.
"My wife is totally not racist but after giving birth she wants to rest and doesn't want the massive celebrations that are customary for the families of the Arab women who give birth," he said.
Referring to the conflict between Israelis and Palestinians, he also tweeted that "it's natural that my wife would not like to lie next to someone who just gave birth to a baby who might want to murder her baby in another 20 years."
He later deleted both tweets.
Smotrich, who lives in a settlement in the occupied West Bank, has long been known for his harsh rhetoric.
His comments were in response to reports that some Israeli hospitals were improperly segregating Jewish and Arab mothers in maternity wards.
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Palestinian and Arab Israeli mothers give birth in Israeli hospitals.
His party leader, Education Minister Naftali Bennett, condemned Smotrich's comments, while others went as far as comparing them to Nazism.
"Knesset (parliament) members are making disgraceful racist statements which were common in Germany in the 1930s," Yair Lapid, head of the centrist Yesh Atid party, said in a statement.
"It's dangerous. Israel has enough external enemies and we cannot afford a political leadership which fans the flames instead of acting responsibility to calm the situation," said Lapid, whose party is part of the opposition.
Smotrich's Jewish Home party forms part of Prime Minister Benjamin Netanyahu's governing coalition, which holds only a one-seat majority in parliament.
The Hadassah hospitals in Jerusalem, which treat Palestinians from east Jerusalem and were mentioned in the report as practising maternity ward segregation, said it took "pride in being medical centres that are symbols of coexistence in every ward and unit."
A statement said they received all patients "with a hug and empathy" but stressed their facilities were attentive to the needs of women who gave birth.