The suspension comes after a heated confrontation earlier between President Donald Trump and Acosta during a news conference.
Reacting to reports of Acosta's credentials being revoked, a furious Hennessey tweeted: "This is a disgraceful and unacceptable attack on a free and independent press. The rest of the White House Press Corp should stand with their colleague @Acosta and refused to participate in any briefing until this appalling decision is reversed."
The sparring between the pair occurred after Acosta asked President Trump about the caravan of migrants heading from Latin America to the southern U.S. border. When Acosta attempted to pose a followup question, President Trump said, "That's enough" and a White House aide unsuccessfully tried to remove the microphone from Acosta's hand.