Brazil team doctor Rodrigo Lasmar said Neymar is making "great progress" after undergoing surgery to fix a broken metatarsal in early March.
Neymar should be able to "regain match fitness" when he takes part in friendlies against Croatia on June 3 and Austria on June 10, Lasmar said.
Dani Alves did not make the squad after picking up a serious injury in Paris Saint-Germain's Coupe de France final victory.
"Dani is a great player and leader and we are going to miss him, but we have other options", Tite said.
Liverpool attacker Roberto Firmino is also included alongside Chelsea's Willian.
Brazil will need him showing all the skills that made him the world's most expensive footballer, with a record €222 million transfer from Barcelona to PSG last August.
"At first, Gabriel Jesus is our starter".
The inclusion of Taison, the coach admitted, suggested Coutinho could be taking a role in central midfield and leaving his spot for Willian. "The challenge is open on the right back, but Danilo has some advantage now because he has performed well recently". Tite said he needs "a pacemaker" in the team, which he has not received from Beijing Guoan's Renato Augusto.