Company founder Elon Musk said on Twitter it is "the first of many solar and battery Tesla projects going live in Puerto Rico."
The Hospital del Nino in San Juan serves approximately 3,000 children around the US territory island and has at least 35 critically ill patients who require care 24 hours a day.
Hospital staff told local newspaper, El Nuevo Dia, at the project was a donation by Tesla.
The hurricane, which made landfall on 20 September, cut power to an overwhelming majority of the island’s residents and forced the hospital to operate off generators while rationing its diesel fuel in the weeks since.
All tree cover protecting the building from the heat was also knocked down during the Category 4 storm that hit last month.
The initiative began with Mr Musk reaching out to Governor Ricardo Rossello. The pair had a conversation on 6 October according to a tweet by the governor saying the teams were “exploring opportunities.”
That same day Mr Musk also took to Twitter to say that a launch of new product would be delayed because the company was “diverting resources…[to] increase battery production for Puerto Rico & other affected areas.”
Tesla Semi unveil now Nov 16. Diverting resources to fix Model 3 bottlenecks & increase battery production for Puerto Rico & other affected areas.
— Elon Musk (@elonmusk) October 6, 2017
By 24 October, Tesla posted a picture on Instagram of dozens of solar panels assembled in the parking lot next to the hospital and Mr Rossello called it a “major contribution”.
A post shared by Tesla (@teslamotors) on Oct 24, 2017 at 6:54pm PDT
— Ricardo Rossello (@ricardorossello) October 25, 2017
At least 75 per cent of the island continues to operate without power or rely heavily on diesel-powered generators, as the Electric Power Authority is operating at 25 per cent capacity.
Estimates put costs to restore full power to the island around $5bn over the next several months.
The contract for power grid restoration worth $300m was given to a two-person firm in Montana called Whitefish, which has come under scrutiny for its ties to the Trump administration and Department of Interior Secretary Ryan Zinke.