This week, India’s Prime Minister Narendra Modi will visit the Indian Ocean island nations of Seychelles, Mauritius and Sri Lanka. New Delhi’s influence in the region has been eroding in the face of a quiet challenge from Beijing—Chinese-built highways, power plants and seaports have appeared in all three countries. With promises of increased civilian and military assistance, Mr. Modi will likely try to reassert India’s influence.

The Indian Ocean has long been considered India’s backyard. Yet China has been busy forging special...