The 29-year-old Scot apologized to fans and said his focus will now be on preparing for the claycourt season, after crashing out in his first match at Indian Wells this week to compound a mixed start to 2017.
According to a schedule listed on his website, Murray's next event is next month at Monte Carlo. He is also the reigning champion of the Italian Open on clay.
"Sadly, due to a right elbow injury, I won't be playing in Miami," Murray said in a statement released by the tournament on Saturday.
"The focus now is on getting ready for the clay season."
Reigning Wimbledon champion Murray, a three-time Grand Slam winner, won the Miami Open in 2009 and 2013 and lost in the final in 2012 and 2015, both times to Serbian star and current world number two Novak Djokovic.
Murray, the 2012 and 2016 Olympic champion, lost to Djokovic in January in the Qatar Open final and endured a disappointing fourth-round exit at the Australian Open, before winning his 45th career title earlier this month in Dubai.
In Indian Wells, the first elite Masters tournament of the season, he was stunned by 129th-ranked qualifier Vasek Pospisil in his second-round opener.
Murray was disappointed with his performance on serve in that match, but said he couldn't pinpoint the problem or blame an injury.
"We wish @andy_murray a speedy recovery and hope to see him back on the court very soon," the Miami Open tweeted.
Murray's decision to drop out of Miami moves 19-year-old American Taylor Fritz into the main draw.
Fritz, who climbed as high as 53rd in the world last year before a knee injury, defeated former US Open champion and sixth seed Marin Cilic of Croatia in the second round at Indian Wells before falling to Tunisia's Malek Jaziri.