Many companies hold employees to a certain standard both in and out of the workplace. This has to do with the fact that, even outside of the office, employees are considered a representation of the company. Therefore, when one of your employees gets arrested -- either at work or on his personal time -- it is not something you can turn a blind eye toward. There are numerous implications to this process that must be considered by you, as an employer.
Consult With Legal
Consult with your company's legal team. Find out if you need to take action, how you need to handle the employee's position (in terms of holding it or letting him go if there is a morals/ethics clause in the employee's contact) and how involved you need to be. Your legal department likely has a protocol for how you should deal with these matters so that your company isn't liable for any action you take as a result of the arrest.
Refrain from commenting about the matter to other employees. They might hear about what happened through word of mouth, but you don't need to speculate on the matter because this will only aid in spreading half-truths and unknown facts. Allow the employee the choice of telling her coworkers what happened or not. It is your responsibility, as management, to ensure that the employee's rights are observed, even by other employees.
Keep Work Flow Moving
Delegate his work to someone else temporarily. Even if he comes back the same day or the next, he still could have some legal wrangling to do. Reassign his tasks so that work is still being completed and his absence doesn't affect the office work flow. Perhaps give him a few of the smaller and less important tasks and responsibilities, in the event that his case doesn't turn out favorably. The key to managing this crisis is to stay focused on production and output.
Treat Employee Fair
Treat the employee fairly and without prejudice. You don't know the entire story of what happened, so it isn't up to you to treat the employee differently. Be aware of her rights at all times, and refrain from passing down judgment or terminating her because of the infraction. Determine if the arrest pertains to the employee's job in any way and use that as guidance in how you deal with the employee upon her return to work.