Not necessary!

From: National Postdoctoral Association:
A QUICK GUIDE TO VISAS AND IMMIGRATION STATUS
FOR INTERNATIONAL POSTDOCS
(Which should also apply to other non-postdoc H1B's)

I would like to travel to Canada or Mexico. My passport has an expired
visa stamp but my other USCIS documents have been revalidated and will be current when traveling. Can I re-enter the United States without getting a new visa stamp in my passport?

If you travel to Canada, Mexico or other contiguous island territories for less than 30 days, it is not necessary to re-enter with a valid H-1B visa if the following conditions are met:

1) you re-enter with a valid I-94 card;
2) your passport is valid for at least six months from date of re-entry;
3) you possess your Notice of Approval; and,
4) you do not apply for the visa at the U.S. consulate.

For appropriate travel documents and instructions, contact your employer’s/institution’s international office.

NOTE: If you are flying to Canada or Mexico, make sure that the airline does not take your I-94 upon your departure. Provide the airline with a photocopy of your I-94.