Betts made the announcement Wednesday night on social media.
"This year continues to be good to me," Betts wrote on Twitter and Instagram. "Can't wait to meet you baby Betts. More life, more blessings!"
Betts made the announcement by customizing a newspaper template called the "Betts Chronicle." The newspaper featured a large headline reading: "Breaking News." It also said "Oh Baby, we got news for you."
Baby Betts is due on Nov. 19.
"Mookie and Bri are brewing a brand new baby and you Betts believe they are excited to share the news," the mock newspaper said.
Hammonds also posted a video to her Instagram, showing off the baby bump and writing "We can't wait to meet you."
Betts, 25, leads baseball with a .340 batting average. The three-time All-Star and two-time Gold Glove winner also has 26 home runs and 58 RBIs for the first-place Red Sox. Betts is a leading candidate for the 2018 American League MVP award.
The fifth-round pick in the 2011 MLB June Amateur Draft has a $10.5 million salary this season and is eligible for arbitration in 2019.