The Scot, who took a surprise wildcard entry to the tournament, received a first round bye and will be up against the Croatian for the third time this season.
Two hardcourt matches have been contested by the players this term, with world number 19 Murray taking the honours in Marseille's Open 13 final and Ancic - currently 51st in the ATP rankings - registering a victory in Miami in March.
Ancic was absent through much of last season, plagued by injuries and illness, but has recently shown signs of a return to form.
Speaking ahead of the match, the 24-year-old was respectful of his opponent, telling the Daily Record: "Murray is an unbelievable player with unbelievable potential - for sure a top-ten player.
"But the two matches we had were both exciting. I know I can play well on clay but I am just trying to find my game a bit, to get back to where I was before my illness."
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