Murray lost to Canadian No.129 Vasek Pospisil in the second round at Indian Wells last week.
In a statement released by Miami Open tournament organisers on Saturday, Murray said: "Sadly, due to my right elbow injury, I won't be playing in Miami".
The top two men's seeds in world tennis won't be competing at the Miami Open, with world No 2 and three-times reigning champion Novak Djokovic pulling out with a right elbow injury. "Apologies to the fans; it's one of my favourite tournaments [he won there in 2009 and 2013 and has had a summer residence nearby for several years]. The focus is on getting ready for the clay-court season".
The Scot will be replaced in the main draw by American world No.136 Taylor Fritz.
Pochettino focused on next Tottenham game - not Arsenal jinx
However, this experiment didn't really work out and then Southampton have mostly played a conventional, if rather narrow, 4-3-3. Spurs have only once had a better overall record at this stage of a top-flight campaign - in their title-winning 1960-61 season.
Murray has surpassed him as world number one and will hold an advantage of more than 4,000 ranking points over his rival come the end of the Miami Open where the victor gets 1,000.
The Serbian joins world No 1 Andy Murray on the sideline, who also withdrew from the tournament with an elbow injury.
The world number two - a six-time victor in Miami - was beaten in the last 16 in Indian Wells last week by Nick Kyrgios, his second loss to the Australian this month. It's the first time the part-time Miami resident will miss the event.
The tournament will, however, have the women's world number one, with Germany's Angelique Kerber posed to return to the summit on Monday despite a fourth-round exit at Indian Wells because of Williams's inactivity.