Yes. In addition to the prohibition against insider trading, company stock held by an "affiliate" (e.g. any director or executive officer) of a public company generally must be sold under SEC Rule 144 and Section 16. These restrictions apply whether the stock was acquired by option exercise or purchased in the open market. For details, see the article series on stock sales by executives.
Most companies, as a matter of corporate policy, have blackout periods. Plus, they prohibit their executive officers and directors from buying, selling, pledging, giving, or otherwise transferring any stock of the corporation without first contacting the company's compliance officer. This requirement may also apply to company securities trades by your spouse as well as relatives living in the same household or whose transactions in company stock you control.