Referee Steve Conroy (left) inspected the Fir Park pitch

The match has been rescheduled to take place on Monday 11 February with a 1945 GMT kick-off.

Well chief executive Ian Stillie said: "After two inspections, we have had to concur with the referee's decision that the pitch was unplayable.

"We are now embarking immediately on major remedial work to make the pitch playable as soon as possible."

Interview: Motherwell manager Mark McGhee

Interview: Dundee chief executive Dave MacKinnon

The problem area of the pitch in front of the East Stand will be replaced at a cost of �40,000 before Saturday's Premier League match against Kilmarnock.

And Motherwell will upgrade the entire playing surface during the close-season.

This will involve replacing the drainage system, the under-soil heating system and re-laying the entire pitch.

The cup match had been set to take place on Tuesday after falling victim to a waterlogged pitch on Saturday.

"I can't stress how disappointed we all are with yet another postponement," added Stillie.

"We purchased new waterproof covers and laid them on Sunday and they appeared to be having the desired effect.

MY SPORT: DEBATE Give your reaction to the latest postponement

"However, the rainfall in the last three or four weeks has been constant, which has left the turf in a very saturated state which is taking time to properly dry out.

"The drains have been blocked up, which has made it increasingly difficult to cope with the deluge.

Dundee have offered their Dens Park as an alternative venue, but Motherwell would prefer to retain home status.

The eventual winners face a trip to Dumfries to face First Division outfit Queen of the South in the quarter-final on 8 March.

It is the sixth such postponement at Fir Park in the space of two weeks.

Gretna's Scottish Cup tie against Morton was called off on 23 January and Motherwell's league game against Inverness followed three days later.

Tenants Gretna played their rearranged cup game on 28 January at Queen of the South's Palmerston Park instead of risking another Fir Park date.

And another home league game for Motherwell, against Celtic, fell victim to the sodden pitch on 31 January.

Manager Mark McGhee insists that it is the state of the pitch drainage, rather than the groundsharing arrangement with Gretna, that is the problem.

And, while two SPL clubs are now using the stadium, Motherwell's reserves no longer play there.

Scottish football is facing a major backlog of fixtures following severe rain and frost during January.

In addition to the three SPL matches involving Motherwell, Rangers have games pending against Celtic and St Mirren.