Payton said that both parties agreed the surgery was a good idea, but that it would not keep the player out for long as he is expected to take part in June's training camp.
"He's having a surgical procedure on his back for a disc," Payton told the Times-Picayune. "It's been asymptomatic but it's something we wanted to do, and he as well, to alleviate any issues coming in the fall.
"He'll be back here in a week. For this next week, he won't be at these OTAs, he'll be going through his rehab. We felt like it would be something that would prevent any issues in the fall."
Byrd played for the Buffalo Bills for five years before joining the Saints.