To ease the misery that the industrial action will cause for thousands of commuters today and tomorrow, the minister said employers should encourage staff to work from home, stagger working hours or arrange alternative forms of transport.
Glenda Jackson said: "I would encourage people to walk or cycle wherever feasible."
Industrial action by members of the Rail Maritime and Transport union has led to the 48-hour halt in Tube services, which began at 6pm on Sunday evening.
Movement of abnormal loads through London will be banned on both strike days to try to keep traffic moving. Highway authorities and public utilities have been asked to minimise roadworks.
The plea may be unnecessary, however, as thousands of workers are expected to stay at home today to watch England's opening game in the World Cup. The London Chamber of Commerce said that a combination of the Tube strike and the football will cost the economy at least pounds 35m on "Idle Monday".
Simon Sperryn, chief executive of the chamber, said: "Others will find alternative ways of travelling but will want to leave early to watch the football or allow extra time to get home.
"If the industrial action continues and either of the British teams progress to the later stages of the World Cup, it could be an extremely costly summer for business."
Britain could be on the verge of a new era of union militancy, the deputy Conservative leader, Peter Lilley, forecast on the eve of the Underground strike.
Mr Lilley told the Welsh Tory conference that there were now signs that the unions were once again "flexing their industrial muscle".
He warned: "From bus drivers in Cardiff to firemen in Essex, Underground employees in London, railway maintenance workers, and broadcast engineers nationwide, there is a creeping return of strike action."Reuse content