It comes shortly after MtGox halted transfers of the digital currency to external addresses after it spotted what it called "unusual activity".
The halt resulted in a sharp decline in the value of Bitcoins.
Last week, MtGox - one of the largest Bitcoin exchanges - said customers should be able withdraw funds "soon".
Meanwhile, all tweets on MtGox's Twitter account have also been deleted.
The Bitcoin Foundation said that Mr Karpeles's resignation would be "effective immediately".
It is the foundation's second high-profile resignation in the past month.
Another board member, Charles Shrem, stepped down in late January after being arrested and charged with money laundering in connection with his Bitcoin company.Continue reading the main story How Bitcoin works
Bitcoin is often referred to as a new kind of currency.
But it may be best to think of its units being virtual tokens rather than physical coins or notes.
However, like all currencies its value is determined by how much people are willing to exchange it for.
To process Bitcoin transactions, a procedure called "mining" must take place, which involves a computer solving a difficult mathematical problem with a 64-digit solution.
For each problem solved, one block of Bitcoins is processed. In addition the miner is rewarded with new Bitcoins.
This provides an incentive for people to provide computer processing power to solve the problems.
To compensate for the growing power of computer chips, the difficulty of the puzzles is adjusted to ensure a steady stream of about 3,600 new Bitcoins a day.
There are currently about 11 million Bitcoins in existence.
To receive a Bitcoin a user must have a Bitcoin address - a string of 27-34 letters and numbers - which acts as a kind of virtual post-box to and from which the bitcoins are sent.
Since there is no registry of these addresses, people can use them to protect their anonymity when making a transaction.
These addresses are in turn stored in Bitcoin wallets which are used to manage savings.
They operate like privately run bank accounts - with the proviso that if the data is lost, so are the Bitcoins owned.
Mr Shrem, the chief executive of New York-based Bitcoin exchange BitInstant, has pleaded not guilty.Dispute
The issues with MtGox had sparked a dispute between the exchange and the Bitcoin Foundation.
The Tokyo-based firm said that its investigation into the unusual activity revealed a loophole that could be exploited to fool the transaction process into sending double the correct number of Bitcoins.
It also left it vulnerable to attacks, which slowed down the rate at which coins could be bought and sold.
As it halted the withdrawals, MtGox had suggested that a flaw in the virtual currency's underlying software was to blame for the problem.
"A bug in the Bitcoin software makes it possible for someone to use the Bitcoin network to alter transaction details to make it seem like a sending of Bitcoins to a Bitcoin wallet did not occur when in fact it did occur," it had said in a statement.
"Since the transaction appears as if it has not proceeded correctly, the Bitcoins may be resent."
However, Gavin Andresen, chief scientist at the Bitcoin Foundation, denied the problem was its fault.
"The issues that MtGox has been experiencing are due to an unfortunate interaction between MtGox's highly customised wallet software, their customer support procedures, and an obscure (but long-known) quirk in the way transactions are identified and not due to a flaw in the Bitcoin protocol," he told the BBC earlier this month.