The 33-year-old, who plays Betty Draper on the AMC drama, welcomed a baby boy named Xander Dane on Tuesday.
Although Jones may have only just become a mother, Weiner told E! Online that the Mad Men team were already getting excited about her return.
"She's doing great," he confirmed. "I think it was a long labour. She is going to be welcomed with tremendous enthusiasm when she comes back."
On Jones's decision to continue filming Mad Men late into her pregnancy, Weiner added: "She's a very athletic person so I don't think she had that hard a time with it. It was great to have her there."
Mad Men star Elisabeth Moss said this week that she believes Jones will make "a great mum".
"We're all so proud of her and happy for her," she added. "We're all really excited to meet the baby."