Simmonds picked the injury up during the victory over Wales at the weekend, and although it is not a serious one, Jones has confirmed the number eight will miss the forthcoming games in Scotland and France.
Jones did go on to say that Simmonds should be available for the game against Ireland, and in the meantime Nathan Hughes will slot into the England side after recovering from a knee injury.
"He's back fit, fresh, but has plenty of work to do," Jones said of Hughes.
Meanwhile, England continued their preparations for the Scotland match, and the rest of the tournament with a 'scrummaging' session against Georgia on Tuesday and Jones was delighted with how the session went.
"They won the early part and maybe we won the later part, so if it was a boxing match it would be a draw," Jones said.
"The Georgians scrum in a quite unique way, and they are able to transfer pressure without moving their feet, so our front-rowers will have learned a lot today. It was a great learning experience for us."