I discovered my employee was arrested for drug and gun possession. Her job's nature  prohibits drug felons. Can she be terminated for this? ?

How many people are arrested but never go to trial or end up with no conviction?  She isn't a "felon" unless she has been convicted.  If she has been convicted of a drug related felony, I don't see any alternative to termination.

In the USA you can fire any employee for any reason or giving no reason at all. If they have a problem with that, there are various ways they can try to get compensated, depending upon circumstances.  We don't know what your employment contract or local laws may say about "arrested" versus "convicted felon". Not all gun or drug possession crimes are felonies, even if she were convicted.

You're the "employer," you tell us.  It would help to know what state or country you're referring to.

I don't know WHERE you are.  I don't know if she's been arrested and/or found guilty.  I'd suggest that YOU read your employment policy if she's YOUR employee and follow company policy.

No idea where in the world you are to know which laws may apply. And we don't know what any employment contract may say as well.

For the moment, being arrested does not make someone a convicted felon. But most employment is at-will.

Depends on where you are.

In most states an employee can be fired for any reason.  But the employer would have good cause if the employee lied on their application.

Most likely but it might depend on whether or not it was mentioned in the job description. Whether or not you told her about it if it’s not mentioned. Whether or not she lied on the application. 

If it’s mentioned in the job description that you must not be a drug felon and she applied, then she can be fired because she lied. 

If you told her that she must not be a felon and she didn’t tell you that she’s a felon then you can fire her. 

If you ask her if she’s a felon and she said no, then you can fire her for knowingly lied about being a felon. 

If there’s nothing mentioned about a felon not qualifying then you might have a hard time firing her since she did nothing wrong. 

If you knew the job requires a person to be felony free, why didn’t you do a background check before hiring her. 

IF you apply the adage, "you are innocent until proven guilty", you might wait for a conviction.  Alternately, you could have a discussion with her, if she admits to possessing or taking drugs, I would certainly think firing is an alternative.  Also, even if convicted, it may not be a felony.

Of course she can be terminated, for this and almost any other reason.