Justice Minister Eveline Widmer-Schlumpf has taken over the finance portfolio ad interim after the incumbent Hans-Rudolf Merz suffered a heart attack.
A permanent solution, including a resignation or a cabinet reshuffle, has to be found within three months according to law.
Merz suffered a heart attack on Saturday in his hometown of Herisau in eastern Switzerland and lost consciousness. He was flown on Sunday to Bern University Hospital where he underwent a multiple bypass operation.
"It is possible to govern with only six, instead of seven members, for a long time. But it is not ideal and not legal," said Interior Minister Pascal Couchepin, who also holds this year's presidency.
"There is no urgency to take further measures," he said.
He refused to speculate on the impact of Merz's absence on the cabinet make-up or December's scheduled election of the Swiss president for 2009. It is Merz's turn to take over from Couchepin in the post which rotates annually.
Under Swiss law parliament has to elect a new cabinet member at its next session – up to three months - following a regular resignation of a cabinet minister, Couchepin told a news conference in Bern on Monday.
Cabinet ministers are elected by parliament for a four-year term, at the end of which their re-election is usually a formality. In case of mental incapacity their family takes the formal decision.
It is not clear yet how long Merz will be in hospital and when and if he can resume his tasks as finance minister.
Doctors said on Monday that Merz is in a stable condition. There had been no complications arising from his operation.
Steps to bring him out of an induced coma would be undertaken on Monday evening and Tuesday, according to chief heart surgeon Thierry Carrel. Merz will probably remain in intensive care for up to two weeks.
Carrel added that it is not yet possible to say whether he will make a full recovery. Further medical tests will be carried out later in the week.
Merz's health problems and insecurity about his political career have fuelled speculation about foreseeable resignations from cabinet.
Defence Minister Samuel Schmid is under pressure by opponents from the rightwing and the centre-left over army reforms and controversial personnel appointments. Should Merz be unable to assume the duties of Swiss president in 2009, Schmid would in principle be next in line.
The longest-serving cabinet member, Transport Minister Moritz Leuenberger, has been in office since 1995, while the oldest cabinet member, 66-year-old Couchepin, has served for ten years.
In a recent newspaper interview Merz said he planned to step down before the end of his second term in 2011.
Merz has been finance minister since 2004. The 65-year-old former business consultant and member of the centre-right Radical Party - a party close to the business community, served as senator before his election to the cabinet.
He has a reputation as a proponent of a strict budgetary policy and is seen as a champion of bilateral relations between Switzerland and the European Union, but not as a supporter of Swiss membership of the EU.
swissinfo, Urs Geiser
The finance ministry is in charge of tax and customs, as well information technology.
Its portfolio includes the Federal Personnel Office and the managment of the federal administration buildings.
The ministry has about 9,000 employees.
In addition to their own portfolios, the seven Swiss ministers each deputise for one of their colleagues. Eveline Widmer-Schlumpf is deputy head of the finance ministry.
Merz, who is 65, is the second oldest member of the seven-strong cabinet.
He has served as finance minister since his election in 2003 and is due to take over the rotating post of Swiss President next year.
Over the past few decades, several cabinet minister have suffered serious health problems. In 1983 then finance minister, Willi Ritschard, died in office.