The exchange announced in February that hackers had stolen hundreds of thousands of bitcoins from it, worth about $500m (Â£300m).
It later said that it had found a substantial number of the bitcoins and had hoped to find a way to continue as a business and pay back customers.
But the court dismissed this plan and appointed an administrator.
In a statement on the exchange's website the administrator said that bankruptcy proceedings were likely to follow.
This would involve MtGox customers being asked to make any claims through the court, although the administrator pointed out that there was no time frame for this process at the moment.
Customers can continue to check the balance of any bitcoins they have with MtGox but are warned that this is not necessarily the amount they would receive as the result of a claim.
MtGox said at the time it went offline that the bitcoins had been stolen from its system by hackers who exploited a loophole in the software that oversaw the Bitcoin system. The administrator said that it plans to investigate the missing bitcoins as part of its role.
The founder of MtGox, Mark Karpeles, refused a request by a US court to attend a hearing this week to answer questions about the collapse of the exchange. He has not been charged with any crime.
The bitcoin is currently trading for around $500, down from a high of more than $1,100 last year.
MtGox, once the world's biggest Bitcoin exchange, has been placed in administration by a Japanese court.