Over 30,000 tickets have now been sold for the match on Saturday, March 30, which kicks off at 12.45pm.
The Capital club previously held the record for the largest crowd at this stage of the tournament when 37,882 people turned out for their match against Toulouse in 2012. English giants Saracens surpassed that figure the following year when 37,888 attended their tie with Ulster at Twickenham.
With the match against Munster fast approaching, head coach Richard Cockerill has urged Capital rugby fans to back his charges against the two-times champions.
“A lot of the players that stepped up for Scotland in the Six Nations are Edinburgh men, so we’ve got a good team and a forward pack that’s able to dominate the opposition,” said Cockerill.
“Hopefully we’ll get a record crowd for the quarter-final next Saturday. We’ve got a team worth watching and we’ve shown we’re a good side. Come and support us. The boys deserve it.”
Tickets are available for the Edinburgh-Munster match from edinburghrugby.org now.