The law, passed by the Israeli parliament on Thursday, denies Palestinians from the West Bank and Gaza Strip citizenship or residence if they marry Israelis.
Under Israeli law, other nationalities are eligible for citizenship or residence when they marry Israelis.
"We will have to look at that very closely," US State Department spokesman Richard Boucher said.
"We certainly oppose any laws that discriminate against individuals for ethnicity, or race or sex, disability and we will have to look carefully at this law and see how it fits under the standard views that we have on this."
The law, voted in for a year, sent shockwaves through the Israeli opposition and parties representing the Arab community, which accounts for 18 percent of Israel's population.
"We think this law is a racist law... interfering in the personal lives of people, their right to fall in love with somebody else. This situaiton will not be acceptable," said Jafar Farah, head of the Mossawa centre for Israeli Arab rights.
Mossawa says 21,000 families will be affected by the measure which targets only Palestinians and does not apply to marriages between Israelis and other nationalities.
Jewish identity eroded
The vote is being seen as the latest expression of a fear that the Jewishness of the Zionist state is being eroded.
"Israel needs to protect its identity as a state," Israeli analyst Eitan Gilboa said.
"The Palestinians are exercising their right of return without mentioning it. You have marriages that are not really marriages. They are done only to allow some people to move into the country."
Israelis says the natioanlity ban
is a response to human bombings
He said the decision, which also blocks the reunification of families split between Israel and the occupied territories, stemmed from a human bombing in Haifa by a Palestinian who acquired citizenship by marrying an Israeli Arab woman.
Likud member Gideon Ezra said that 30 Israelis have been killed by Palestinians who gained Israeli citizenship through marriage since the start of the intifada 34 months ago.
He also said 100,000 Palestinians have become Israelis by tying the knot since the 1993 Oslo accords.
There is a deep fear among government members and many Israelis over the country's future as a truly Jewish state.
The same apprehension can explain the fierce opposition of Israeli Jews to the Palestinian right of return, which could swing the demographic balance in the Arabs' favour.
Theoretically, if the Palestinians who fled or were expelled during the 1948 war and their descendents came back to Israel, the country would witness an influx of 3.7 million Palestinians.
Israel could also be confronted by mass immigration from the West Bank by Palestinians fleeing poverty and unemployment, Eitan Gilboa said.
"Even in a state of peace, because of the economic disparity between Israel and its neighbours, it would be important to control free movement of people from one place to another.
"If you allow the influx of hundreds of thousands of Arabs from the entire Middle East into the country, then this (Israel's) identity is going to be compromised."