Coach Sean Payton declined Monday to offer any injury details about Goodwin, who was hurt during Sunday's 20-9 victory over the Minnesota Vikings.
In the meantime, the Saints will turn to second-year pro Tim Lelito, who spent much of the summer with the first-string offense while competing with Goodwin for the starting job.
"I think we felt the whole time like we had two starters, and whoever they named the opening day starter was fine with us," Saints offensive tackle Zach Strief said. "We feel good about both of 'em. And hopefully we'll get Goody back sooner than later."
Although Goodwin got off to an excellent start this season, Strief said "nothing changed" this past Sunday after Lelito came into the game following Goodwin's injury in the third quarter.
There was one blip, obviously, since Lelito sailed a shotgun snap high and wide past quarterback Drew Brees on his first play. But after that, Lelito said, he settled in.
"He played well, settled in and did some good things," Payton agreed. "That competition, shoot, it existed at least halfway through training camp or two-thirds of training camp. ... So the snaps obviously that he's had, the work that he's had, certainly helped him yesterday."
Lelito presumably will make his first career start at center Sunday night against the Dallas Cowboys. He made two starts at guard last season for the Saints as an undrafted rookie out of Grand Valley State.
"I prepare every week like I'm going to start just in case anything does happen throughout the week," Lelito said. "There's never any time, especially in the NFL, where you can just be like, 'Oh, I'm a backup, so I don't have to prepare at all.'"
After Sunday's game, Brees said "there's a big comfort level" with Lelito. And Brees said he was as much to blame for the missed connection on the snap.
"Listen, I gotta play shortstop," said Brees, who went to Lelito to encourage him after that play. "I can't let those balls get by me. I don't care if they're low, high, coming in hot, whatever. That's my job. So I'm as mad at myself as anybody."