It depends on the circumstances. If an employee injures someone while carrying out his job, the company will almost certainly be liable to the injured person. For example, if a delivery driver for a florist hits a pedestrian while rushing around making deliveries on Valentine's Day, the pedestrian can sue the company for damages. At the other extreme, if an employee hurts someone while off-duty, with no connection to work, the company won't be liable. For example, if that delivery driver sings in a band on the weekends and injures a fan by knocking over a tower of amps, the company can't be sued.
Your company may also face liability if it hires or retains an employee whom it knew -- or should have known -- posed a danger to the public. For more information on when employers can be sued for injuries caused by employees, see Nolo's article Employer Liability for an Employee's Bad Acts.