The Scot, who reached the final at SW19 for the first time last year, was drawn in the same half as fifth seed Rafael Nadal, but he is likely to not have to play the two-time champion until the semi-finals.
Defending champion Roger Federer was pitted against Romanian Victor Hanescu in this morning's draw and is likely to meet Nadal in the quarter-finals.
Number one seed Novak Djokovic will play Florian Mayer while Nadal's first match will be against Belgian Steve Darcis.
Murray beat Becker in straight sets last week when he played the German in the AEGON Championships at Queen's.
That is the only time the two have met. Becker is ranked 95 in the world and hails from Merzig.
The 32-year-old has won just one career title since turning professional in 2005 and has accrued around $25 million (over £16million) less in winnings throughout his career.
If Murray's draw goes to form, he will meet Jo-Wilfried Tsonga in the quarter-finals, who he beat in the last four to reach the 2012 final.