Heyward left during the sixth inning of Wednesday's 4-1 win over the New York Mets after being hit in the face by a pitch from the Mets' Jonathan Niese at Citi Field.
The outfielder walked off under his own power, but was later hospitalized after spitting up blood.
Heyward was diagnosed with a jaw fractured in two places, with a possible return date of 4-6 weeks, the newspaper reported.
That timetable would wipe out the rest of the regular season for the Braves' outfielder, who is batting .254 with 13 home runs and 37 RBIs.
Since being moved to the lead-spot spot 21 games ago, Heyward has posted a .357 average for the National League East leaders.
Ohio bar shooting arrested, charged with murder
Duggar sisters unveil Christian dating rules in new book