The airline had suffered years of financial losses even before it was hit by two major disasters in 2014.
Flight MH370 disappeared on its way from Kuala Lumpur to Beijing and is still missing, while MH17 was shot down over eastern Ukraine.
Mr Mueller said he was leaving due to "changing personal circumstance."
He took up his role in May 2015 to oversee a $1.56bn (Â£1.1bn) turnaround plan which included massive job cuts and dropping unprofitable destinations.
"We are very disappointed to lose Christoph as CEO but we fully understand his reasons and respect his need to do this," Malaysian Airlines Chairman Md Nor Yusof said.
Mr Mueller will continue to serve until September 2016 and will stay on the board as a non-executive director.
The carrier has already begun to look for a new chief executive and says it is considering both internal and external candidates.
It said that Mueller had set up a strong management team which would be the foundation for a successful turnaround.

The gang were responsible for more than 35 thefts across Lincolnshire, Leicestershire, Nottingham and Yorkshire over 11 months in 2013.
Lincoln Crown Court heard how the gang targeted three major rail improvement projects being delivered by Network Rail, and stole signalling cable.
They then stripped the cabling and sold the copper inside.
The men targeted sites where Network Rail were carrying out work to upgrade signalling.
Gordon Aspden, prosecuting, said "It was organised, well-planned and professional thieving.
"Over 11 months between February and December 2013 the defendants were responsible for the large-scale theft of power cables being used in these projects. Most of the thefts took place in isolated locations.
"There is a strong suggestion that at least one person with inside information, an employee within the rail network, played some part in providing information to these defendants."
He said: "Once cabling was stolen it was stripped of its sheathing. It was a very valuable commodity. It was sold as scrap to dealers. The total cost to Network Rail was in excess of £1m. That figure dwarfs the sums these defendants gained."
Mr Aspden said that on one occasion the line between Lincoln and Spalding had to be closed for two days following a theft at Sleaford that cost Network Rail £23,000.
Recorder Simon King, passing sentence, told them: "I have no alternative but to impose immediate custodial sentences. This was organised and professional thieving. It was plainly worth your while to engage in that."
Malaysian Airlines chief executive Christoph Mueller has resigned after less than one year of leading the carrier's reorganising efforts.
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Six men, including five from the same family, have been jailed for conspiracy to steal railway cable.