Vianney Hennes was France Telecom's representative on the board, and has apparently resigned as part of the war of words about the cost of upgrading Mobilcom's network to cope with advanced third-generation traffic.
France Telecom bought 28.5% of Mobilcom in March 2000 for 2.8bn euros ($2.7bn; £1.7bn).
The French company's stake is held through its Orange mobile phone subsidiary, and carries with it an obligation to fund Mobilcom through to the start of 3G services.
Holding back
But its heavy debt burden means France Telecom has made it clear that it wants greatly to slow down the pace of investment.
Mobilcom does not agree, and the two sides are unable to agree on a business plan.
"Any such obligation is subject to the mutual agreement between France Telecom/Orange and (MobilCom Chairman Gerhard) Schmid on fundamental matters, including the business plan and the budget of MobilCom," Orange and France Telecom said in a statement.
Mr Schmid told Suddeutsche Zeitung on Monday that he has an option to force France Telecom to buy a third of his 43% stake in MobilCom at any time.
The German carrier faces an intensely competitive mobile market, with six operators set to jockey for position once 3g arrives.
France Telecom and Orange added that they expect MobilCom to adopt a business plan which reflects recent changes in the German mobile communications market, and which includes "substantially reduced" capital expenditure.