Possibly. Whether an employer can terminate your employment for starting a business depends on your employment agreement, company policies, the nature of your side business, and the laws that apply where you work.
Starting a business does not automatically mean you can be fired. However, problems may arise if your side business competes with your employer, uses confidential or proprietary information, solicits your employer's customers or coworkers, misuses company resources, or interferes with your job responsibilities. Your employment could also be affected if your business violates confidentiality, non-solicitation, or non-compete agreements (where enforceable), or other legal or contractual duties you owe to your employer.