Embiid had surgery last week to repair a stress fracture in his right foot, and could miss anywhere up to a full season depending on how rehabilitation goes.
He was not able to attend Thursday night's draft due to recovery from the surgery.
"It's a very exciting day for me and my family," Embiid said in a statement to ESPN's Andy Katz before the draft. "A lot of hard work has gone into my journey to be here today and I am truly blessed to be able to realize my dream of being drafted. While I wish I could be in New York, I'm happy that my family is here with me to celebrate with me. I'm more determined than ever and looking forward to getting back to work with my new team."
The versatile 7-footer had a fantastic freshman season with the Jayhawks, averaging 11.2 points and 8.1 rebounds while blocking 72 shots to earn Big 12 defensive player of the year honors.
Embiid already had some health questions, mostly regarding a balky back. Now he's had foot surgery and could be out for up to six months.
The Sixers also had the 10th overall pick in the draft. They also have the Nos. 32, 39, 47, 52 and 54 overall picks.
Information from the Associated Press was used in this report.
76ers Draft Embiid No. 3
The Philadelphia 76ers selected Kansas center Joel Embiid with the No. 3 pick.