One message on Centcom's Twitter feed said: "American soldiers, we are coming, watch your back."
It was signed by Isis, another name for the Islamic State. Some internal military documents also appeared on the Centcom Twitter feed.
Centcom said it was "cyber-vandalism" and not a serious data breach.
In a statement, it said there was no operational impact and no classified information was posted.
"We are viewing this purely as a case of cyber-vandalism," it said. Later on Monday, its Twitter feed became visible again, although not active.
Embarrassingly, the hack happened as President Barack Obama was giving a speech on cyber-security.
Reflecting on major breaches like a recent hack of Sony Pictures, Mr Obama said in his speech the US had been reminded of "enormous vulnerabilities for us as a nation and for our economy".
His spokesman Josh Earnest said the US is looking into the Centcom hacking.
He said they were investigating the extent of the incident, and that there was a significant difference between a large data breach and the hacking of a Twitter account.Analysis - Jonathan Marcus, BBC defence correspondent
This is an irritating hack rather than a matter of major security concern, but it will inevitably lead to a review to see if there are any more fundamental vulnerabilities in the US military's public facing web and Twitter accounts.
The material posted on the site represents an amateurish and unconvincing attempt to publicise "secrets". Most of the information is hardly secret at all - the postal address at the Pentagon of the Chairman of the US Joint Chiefs of Staff, General Martin Dempsey.
A variety of maps and diagrams were also posted by the hackers. Two appeared to be slides from a presentation at the Lincoln Laboratory - a government funded think-tank at the Massachusetts Institute of Technology.
They showed maritime defences on the Chinese coast, but not in any great detail. There were also simple maps of North Korea showing population centres, nuclear installations and missile sites.
You can find maps showing the same things on the websites of many US think-tanks.
An unnamed Pentagon official told Reuters the hacking was an embarrassment but did not appear to be a security threat.
And Professor Alan Woodward, from the University of Surrey, said he did not consider the attack to be a major breach of security.
"I wouldn't say it's trivial, but it's just a slip," he told the BBC.
"Twitter accounts are usually looked after by an individual in an organisation - it's very easy to give away that password.
"In terms of if this is a hack into something secret, or sensitive - no, it's not. An individual has made a slight mistake."At least one of the documents "leaked" was previously available on Pentagon's website
Subsequent posts on the Centcom Twitter account said: "Pentagon Networks Hacked! China Scenarios" and "Pentagon Networks Hacked. Korean Scenarios."
Some of the documents posted appeared to list names and phone numbers of members of the military as well as PowerPoint slides and maps.
The Centcom YouTube account was also hacked.
American and coalition war planes have been undertaking air strikes against IS in Iraq and Syria.