It depends - sometimes employees must sign a 'non-compete' agreement when they take a job. If that's the case, then you should check the language in the agreement.
Either way, you may want to consider this: if you were the manager and knew that your employee was working for a competitor, what would you think? My guess it that you wouldn't be crazy about it... so, if there are any options to work in another type of job, that's what I'd suggest you pursue. (but that's just my opinion!) Good luck!

You might be OK if there franchises but you wanna be careful. Years ago I worked for a national retailer that had strict policies about working with competitors or other retailers that offered similar products. I don’t think it’s a firing offense but you could be asked to choose one over the other. Take a look at the employee manuals for both companies.