The 38-year-old actor and Wilde, 30, were blessed with a son Oti in April, reported Contactmusic.
"Jason was in the delivery room for Olivia, but witnessing and assisting in the birth suddenly became too overwhelming when he took one look at his child starting to be born, turned pale, mumbled something to a nurse and then went down for the count," a source said.
Sudeikis was worried that he had missed his son's arrival after regaining conscious, but was assured by two nurses that he had not.
