The major leagues conclude the month of June with a record of 1,101 homers hit during the month. This beats the previous record of 1,069 set in May 2000. The sluggers doing the most damage are rookie Cody Bellinger, who led all batters with 13, George Springer, who hit 11, and Justin Smoak and another rookie, Aaron Judge, smashing 10 each. 77 batters had multi-homer games, including a four-homer game by the unlikely Scooter Gennett on June 6th.

On June 30, 2017 The major leagues conclude the month of June with a record of 1,101 homers hit during the month. This beats the previous record of 1,069 set in May 2000. The sluggers doing the most damage are rookie Cody Bellinger, who led all batters with 13, George Springer, who hit 11, and Justin Smoak and another rookie, Aaron Judge, smashing 10 each. 77 batters had multi-homer games, including a four-homer game by the unlikely Scooter Gennett on June 6th.

Source
Baseball Reference June 30