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."
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.