He did not give a reason for the suspension, which was pending as a result of the inquiry, and did not provide further details.
USA Today reports that a Twitter account named Woleski posted abortion rights rulings last month.
Wade responded to a statement from the first lady following the Supreme Court's decision to dismiss her.
"For very nearly 50 years, ladies have reserved the privilege to settle on their own conclusions about their bodies. Today, that right has been taken away from us," Biden said.
The newspaper reported that a tweet from Wolesky's name said: "You are finally happy to know what a woman is." The tweet was later deleted.