They were one of 12 foreign consortiums short-listed by the former army-ruled country to bid for two licences to build, own and operate a nationwide network for an initial term of 15 years.
The two companies said in a statement that they had decided to pull out because "the opportunity does not meet the strict internal investment criteria to which both Vodafone and China Mobile adhere".
"Vodafone and China Mobile will continue to watch Myanmar's progress with interest and will give due consideration to any future opportunities that would meet the companies' investment criteria," they added.
One bidder has estimated the required spending to develop a Myanmar network at about USD 2 billion.
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Applicants also face a list of requirements, including to provide mobile voice services to 75 per cent of the country geographically within 60 months.
Less than 10 per cent of Myanmar's population has access to a telephone -- a figure the government hopes to boost to 80 per cent by 2016.
Other companies on the shortlist include Orange, KDDI, SingTel and a consortium backed by an investment fund linked to billionaire George Soros.