Enemkpali broke the starting quarterback's jaw in two places Aug. 11, and Smith is expected to miss the first month of the season.
Smith, who had screws and metal plates inserted into his jaw, said he has been pain-free for two or three weeks.
Speaking to media for the first time since he was injured, Smith did not say much about the incident with Enemkpali, who was released by the team immediately afterward.
"I just want to move on. That's what I've done," said Smith, who did not reveal whether the linebacker apologized to him or whether Smith paid the $600 thought to be the source of contention.
Enemkpali previously said he punched Smith because he was upset the quarterback had not repaid him for airfare and limousine fees after Smith skipped the linebacker's football camp in Texas in July.
"There's still an (NFL) investigation being done," Smith said, "so it's not really important for me to say anything about it. That will clarify more things than anything."
With Smith out, Ryan Fitzpatrick will start for the Jets, who open against the Cleveland Browns on Sunday.
Enemkpali was picked up by the Buffalo Bills after the Jets waived him, but he didn't make the Bills' 53-man roster. The Bills signed him to the practice squad on Monday though.