Yuma County Sheriff's Office spokesman Alfonso Zavala said the bus had been on a dirt road near a field and tipped over while attempting to turn on an embankment.
It was carrying 52 people, including 23 who were hurt.
Two were flown to Phoenix-area hospitals from the crash site, Zavala said. None of the injuries appeared to be life-threatening.
The other 21 people hurt were taken to a hospital in the nearby border town of Yuma, about 150 miles east of San Diego. Four were in serious condition Thursday afternoon, Yuma Regional Medical Center spokeswoman Jenn Lotz said.
One of those patients will be transferred to a trauma centre in Phoenix.
Most of the patients suffered minor injuries, according to the hospital. The facility also treated three others who were not among those initially transported from the scene.
The patients ranged from 27 to 82 years old, Lotz said. No other details about the injured were released.
It's too early to say what caused the morning crash, Zavala said, but it appears the bus's back tires went into soft, sandy soil on the embankment. The bus had been on a dirt field-access road and was trying to reach another road alongside a canal.
The sheriff's department is investigating.
Agriculture tours are quite common in Yuma, known as the "lettuce capital of the world."
The group was on a Field to Feast agriculture tour organized by the Yuma Visitors Bureau. The agency said in a statement it was "extremely sorry that this accident occurred."
The tourism office conducts the tours between January and March to showcase local produce. Tours include a narrated motorcoach ride through farm fields, along with lunch made from locally grown food.
The bus crash occurred as the group was viewing a field of cabbage and celery crops, Zavala said.
Uninjured passengers were taken back to their cars at the Yuma Quartermaster Depot State Historic Park, according to the Visitors Bureau.
The bus is operated by Phoenix-based Tour West America. A woman who answered the phone at the company's Yuma tour office said officials were still trying to gather information.
According to its website, Tour West America provides charter service and tours via motorcoach in metropolitan Phoenix, Yuma and surrounding lower Colorado River cities. The company also offers vacation and cruise packages.
Tour West America originated in Yuma in 1986.