The fight against Teixeira was to be Jackson's final bout with UFC.
"Rampage is hurt and is out of UFC 153 in (Rio de Janeiro)," White said on Twitter.
Jackson (32-10) has lost two fights in a row.
He suffered a knee injury before his most recent fight against Ryan Bader on Feb. 26 in Saitama, Japan. The injury hindered Jackson's training and he was unable to make the 205-pound light heavyweight limit.
It was the first time Jackson failed to make weight in his professional mixed-martial-arts career.
Jackson and Bader competed at a catch weight of 211 pounds. Bader won the fight by unanimous decision.
The hard-hitting Teixeira (18-2) was preparing to make his second UFC appearance. He submitted Kyle Kingsbury in the first round during his UFC debut on May 26.
Teixeira has knocked out 11 of his 20 professional opponents.
UFC has not yet determined who Teixeira will now fight or if he will remain on the Oct. 13 card.