The group, which also took responsibility for hacking Pentagon social media accounts last month, tweeted "#CyberCaliphate Bloody Valentine's Day #MichelleObama! We're watching you, you girls and your husband!"
The FBI is investigating the hacking, White House spokesman Josh Earnest said. He did not comment specifically on the threat to the first family. The FBI had no immediate comment.
The Twitter account showed a head wrapped in a black-and-white scarf next to a banner proclaiming "CyberCaliphate."
The "Je suIS IS" was a reference to the phrase "Je suis Charlie" that emerged last month in support of victims of the attack by Islamic militants on Charlie Hebdo in Paris that killed 12 people.
Newsweek removed the "CyberCaliphate" banner and tweets and regained control of the account within 14 minutes, the magazine said. The Islamic State militant group has seized territory in Iraq and Syria and has declared itself a "caliphate."
The hackers also posted a message intended for the United States in retaliation for its actions in the Muslim world.
"While the U.S. and its satellites are killing our brothers in Syria, Iraq and Afghanistan, we are destroying your national cyber-security system from inside," it said.
The message contained a list of names under the heading "brave mujahideen."
The group took responsibility for the intrusion last month of the Twitter and YouTube accounts for the U.S. Central Command, which oversees operations in the Middle East. The hackers claimed to be sympathetic toward Islamic State, which is being targeted in bombing raids by a U.S.-led coalition.
The attack on Central Command accounts in early January coincided with Obama's announcement of proposals to bolster U.S. cyber-security after high-profile hacking incidents, including one on Sony Pictures, that U.S. officials blamed on North Korea.
The cyber-attack on Tuesday occurred the same day that Obama's counterterrorism coordinator, Lisa Monaco, announced the formation of a new agency to monitor and analyze cyber-security threats.
At the time of the Central Command attack, several current and former U.S. security and intelligence officials said they had never heard of the "CyberCaliphate." They noted that Twitter accounts are more vulnerable to cyber intrusions than many company or federal government websites.
Jim Impoco, editor-in-chief of Newsweek, played down the intrusion.
"They were able to get control of our account for a few minutes. We are working with Twitter to make sure it doesn't happen again," he said.
© Thomson Reuters 2015