Richard Cockerill’s men were due to host the Irish province on Friday night in the Scottish capital.
But the severe wintry weather conditions currently sweeping the UK and Ireland has forced the call-off.
The match will now go ahead over the weekend of March 16-18.
It follows Wednesday’s news that Glasgow’s trip to Belfast on Friday to face Ulster had also been pushed back until the weekend of April 20-22.
In a statement, Edinburgh said: “Threats to travel and the potential of severe weather on the day of the game raised concerns to the health and safety of supporters, match officials, players and staff from both clubs which is always paramount in such situations.
“The severe weather currently being experienced in the UK and Ireland combined with the further inclement conditions forecast for tomorrow night, means that those travelling to BT Murrayfield would likely be exposed to hazardous conditions which raises welfare concerns.
“It is therefore in the best interests of everyone involved to postpone the fixture until the weekend of March 16/17/18. The exact date and kick-off time will be confirmed as soon as possible.
“We hope that supporters understand the reasons behind this postponement and that any inconvenience caused is minor compared to the impact of making this decision closer to kick-off.
“Ticket holders are encouraged to retain their tickets as they will be valid for the rearranged fixture. Further information will be sent to ticket holders via email direct from Edinburgh Rugby.”