Responding to a question on Twitter, the official Overwatch account revealed that Ranked Competitive matches in multiplayer will be in July:
“We’ll be introducing our Competitive Play (hopefully) later in July. Stay tuned!”
A follow-up tweet gave a more specific timeframe:
“We’re aiming for mid-to-late July.”
Previously, Jeff Kaplan of Blizzard noted that the team was currently focused on the Ranked Competitive matches, and that it was their “priority”. With the hope that they would get it out in June. It appears that will no longer be the case.