It comes after a woman reported the theft of her purse while she was attending her ill father in his hospital room.
Days later, police received reports of the theft of three mobile phones, a wallet and some money from patients and relatives of patients and workers.
The suspect, a caretaker who has not been named, was apprehended and police searched him, finding mobile phones that had been stolen that morning on his person.
He was then arrested.
It comes during a recent crime surge in the Andalucian town.
La Linea is a gateway for drugs smuggled from the African continent, and for tobacco smuggled from Gibraltar.
This leads to higher crime levels.
In June, a La Linea Police officer was killed during a tobacco smuggling bust, and several officers have been the victims of violent attacks since.