In January, the Mexico international penned a loan deal until January 2019, and reunited with his former Ibrox manager.
However, Caixinha appears to have run out of patience with Pena, who has barely played after sustaining ankle injury, and was booed by his own fans when he did feature because of lacklustre performances.
Last month, he was caught buying a six-pack of beer while wearing Cruz kit after a training session.
At the end of April, reports suggested that he had had his contract terminated after being caught “urinating in a fountain” while intoxicated.
Caixinha said: “Carlos [Peña] is not going to continue with us, he has heard it directly from me.”
The 28-year-old is under contract at Ibrox until the summer of 2020.
• READ MORE - Carlos Pena ‘sacked after urinating in hotel fountain’