The action alleges that Intermex, a firm which arranges money transfers, tracked employees even when off-duty.
Myrna Arias alleges that she was "scolded" for removing the app and fired a few weeks later.
The company has not responded to the allegations.
According to court documents published by website Ars Technica, employees were instructed to download the app, called Xora, to their phones in April 2014.
Xora is described on its website as a workplace management app which allows companies to "remotely manage" their workers by keeping track of their hours and other aspects of their job.
Xora's website says that the app uses GPS to allow bosses "to see the location of every mobile worker on a Google Map".
According to the lawsuit, Ms Arias's manager "admitted that employees would be monitored while off-duty and bragged that he knew how fast she was driving at specific moments ever since she had installed the app on her phone".
"He confirmed that she was required to keep her phone's power on 24/7 to answer phone calls from clients," reads the court document.
It goes on to detail that Ms Arias had "no objection" to being monitored at work but felt that monitoring her location during non-work hours was an invasion of her privacy.
She likened the app to a prisoner's ankle bracelet.
Her boss "scolded the plaintiff when she de-installed the app in late April in order to protect her privacy", reads the court document.
She was fired on 5 May.
Ms Arias is seeking damages for lost earnings in excess of $500,000.
Mark Weston, a partner at law firm Matthew Arnold & Baldwin, told the BBC that an employer "would not be allowed to track an employee without the consent of that employee".
Clauses that allow for tracking apps would have to be built into contracts, he said.
As for the legality of firing an employee for refusing to use such an app, Mr Weston said: "In the US, things may be looser because many employees there are employees 'at will'. Accordingly, employers have far greater flexibility than in Europe to dismiss an employee who is not playing ball."

Andy Clewes had the transplant in Manchester after his friend Helen Crowther agreed to become a donor.
The 46-year-old suffered chronic kidney disease since birth and was on the verge of needing dialysis treatment.
Mr Clewes and Ms Crowther, 45, are now planning "a curry and a few beers" to celebrate the successful procedure, which was carried out in January.
"I've just got so much more energy now," Mr Clewes, a radio DJ from Crewe, Cheshire, said.
"There was a time when I could sleep 23-hour days, but now I struggle to get myself off to bed.
"It's hard to describe how it feels. Every now and then you remember how lucky you are to have your mate's kidney."
Mr Clewes said the pair would like to get involved in charity work to support others in need of transplants - and may even take on an extreme challenge.
"There are a few organisations who do skydives and things like that, and I've never done something like that before," he said.
"I think it's something I'd like to look at once I'm fully recovered."
Although his strength has returned, Mr Clewes will continue to need regular check-ups and medication to prevent his body rejecting the organ.
But he added: "I'm feeling great. I'm exercising. It's really a life-changing step and I don't want to let Helen down."
Ms Crowther, a charity worker from Runcorn, met her friend at a fundraising event in 2006 and later became "best woman" at his wedding.
She said: "I think Andy's a bit worried he might now take on some of my characteristics.
"I think his wife might like that as he might start tidying up around the house a bit more.
"We met up about four weeks after the operation and just fell back into normal every day chatting really.
"We have plans to celebrate properly and knowing Andy it will probably just be a few beers and curry."
About 3,000 people have kidney transplants each year in the UK and about a third of these are from living donors.
You can find more information on the NHS Organ Donation website.
A US sales executive is suing her employer for invasion of privacy, alleging that she was fired after deleting an app which tracked her movements.
[NEXT_CONCEPT]
A man who was given a kidney by his best friend says he feels "100% better" and is considering a charity skydive.