The incident happened last Friday at Phoenix Sky Harbor International Airport.
Investigators said the device was not a bomb but they are concerned the suspects were conducting a trial run to see if they could get a real bomb through security.
Luwiza Daman, a 51-year-old woman from Ethiopia, had the suspicious item in her carry-on bag as she tried to get through security. She told investigators that an acquaintance gave her the item to be delivered to a friend in Des Moines, Iowa.
The acquaintance, identified as 25-year-old Shullu Gorado of Eritrea, said the package was Ethiopian food with a cell phone strapped to it.
"I didn't know that you could not send food to the airport, that this was illegal. It was just regular food I bought from the store," said Gorado.
A third man, 34-year-old Shani Asa of Eritrea, was also arrested in connection with the incident. According to police, Asa admitted to attaching the cell phone to the container of food.
Police have not identified the Des Moines contact who was supposed to receive the item.
Authorities said they do not have a motive yet but have not ruled out terrorism.
"We're taking it seriously, not just because of the substance they were trying to take on board a plane, but also the 10-year anniversary of 9/11 and the proximity of that date to now," Phoenix police Sgt. Steve Martos said.
Daman, Gorado and Asa all have been booked into Maricopa County jail on a charge of having a hoax device and conspiracy to obtain a hoax device. More charges may be filed as the investigation continues.
The Associated Press contributed to this report.