Police did not release the age or gender of the alleged victim.
According to police, the relationship with the victim had been going on for nearly a year. It was a parent who alerted authorities to the allegations.
Hillcrest Christian School Secondary School Principal Lance Haliday said the school acted swiftly to respond to the situation.
"No student is at risk. The safety and well-being of our students is, and will remain, our number-one priority," said Haliday.
"Take a look at the picture, have a discussion with your kids. If there is a crime or concern, give us a call," said LAPD Capt. Sean Kane.
Police are looking for any other alleged victims. Anyone with information related to the incident is urged to call the LAPD at (877) LAPD-24-7.
Hubbard was released after posting $100,000 bail.
Hubbard had worked at the school for eight years.