In the first instance, you should consult your staff behaviour codes and your company’s social media policy (if it has one).
You need to determine whether the employee’s action constitutes misconduct. In general, comments made on social media are considered to be private activities, so unless you have specific rules in place you’re unlikely to be able to fire someone for this.
You should also talk to the employee. Make sure they realize the seriousness of their action, the repercussions it could have for both their own reputation and that of their employer, and the negative impact it could have on their colleagues.
This may well be a good opportunity to update your staff guidance, and make sure everyone understands the limits of acceptable employee behaviour.