Novartis AG is looking to strengthen its ties with tech startups as giants like Apple Inc., Google and Amazon.com Inc. advance rapidly into the health-care field.

The Swiss drugmaker is setting up innovation labs in cities around the world, starting with San Francisco, Chief Digital Officer Bertrand Bodson said in a phone interview. As part of the new project called the Novartis Biome, the company is collaborating with outfits including Mekonos, a developer of cell- and gene-therapy technology, and Medable, a digital health firm. Both are based in the Silicon Valley town of Palo Alto, California.

“Technology, data...