Jones is expected to miss a minimum of 2-to-4 weeks aftersustaining a right shoulder strain and small low-grade partial thickness tear in his rotator cuff.
Jones (shoulder) won't play during Friday's game versus the Pacers.
Jones (shoulder) will not play in Wednesday's game versus Golden State.
Jones is expected to serve as the Pelicans' starting center this season, Shams Charania of ESPN.com reports.
Jones will start Monday's preseason game against Orlando.
Jones chipped in 18 points (6-9 FG, 4-7 3Pt, 2-2 FT), two rebounds and one assist over 36 minutes during Wednesday's 124-92 loss to the Thunder in Game 2 of the Western Conference Quarterfinals.
Jones produced 15 points (6-10 FG, 1-2 3Pt, 2-2 FT), four rebounds, three assists and three steals over 38 minutes during Friday's 111-109 loss to San Antonio.
Jones supplied 16 points (4-12 FG, 2-8 3Pt, 6-6 FT), two rebounds, four assists, one block and one steal over 31 minutes during Tuesday's 119-112 loss to the Thunder.
Jones closed Tuesday's 104-91 win over the Nets with 11 points (4-8 FG, 2-5 3Pt, 1-1 FT), three rebounds, three assists and three blocks over 34 minutes.
Jones (hip/back) is available for Tuesday's game versus the Nets, Christian Clark of The New Orleans Times-Picayune reports.