The Australian Competition and Consumer Commission fined the US car brand $155,460 for failing to meet the standards under consumer laws between June last year and May this year.
Ten infringement notices were issued to Tesla over three of its key fobs as well as two illuminated strips around car doors.
Two of the three key fobs have since been tested and found to be safe.
The infringements come more than a year after the ACCC introduced new product standards for button batteries following the deaths of three children who swallowed or inserted the small batteries.
ACCC deputy chair Catriona Lowe said the standards were designed to ensure products that used button batteries were tested for safety before they were sold and that companies included explicit warnings on product packages.
"Any failure to test these products before they are sold poses an unacceptable risk to children," she said.
"We expect all companies, large and small, to comply with the mandatory button battery standards to ensure children are protected from the dangers of button batteries."
Tesla's 10 infringement notices affected key fobs for its Model 3, Model Y, Model X and Model S electric vehicles, as well as illuminated door sills in Model 3 and Model S cars.
The ACCC alleged the key fobs were not tested before sale, while the door sills did not feature the mandatory safety warnings.
Tesla Model 3, Y and X key devices have since met safety standards but other products were still being tested.
"Key fobs are often in easy reach and can be attractive to children so if the battery compartment is not secure and the batteries become accessible they pose a very real danger to children," Ms Lowe said.
The ACCC said Tesla co-operated with its investigation, had issued safety information to affected customers, and would implement an annual compliance review.
The fine is the third and largest penalty issued for failing to meet the button battery safety requirements that were introduced last year.
In May, discount retail chain The Reject Shop paid a penalty of $133,200 for failing to test two novelty Halloween pumpkin products before sale.
Homewares store Dusk also paid a penalty of $106,560 for failing to test or warn customers about the use of button batteries in four novelty Halloween products that it subsequently recalled.
Button or coin batteries can cause significant injuries if swallowed and can burn tissue or organs within as little as two hours.
Anyone who suspects a child may have swallowed a button battery is urged to call the Poisons Information Centre on 13 11 26.
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