Police commander Rolando Casanueva says the first bomb went off late Tuesday. It was apparently made from an unknown powder taken from a fire extinguisher, and was left in a backpack on a stairway.
Casanueva said Wednesday it broke windows but nobody was hurt.
The second device went off an hour later in another gym, without causing any serious damage.
Nobody has claimed responsibility. Similar attacks in the past have been linked to anarchist groups.
They occurred one month before the anniversary of a 1973 military coup, a date often preceded by unrest and minor attacks with explosive devices.