"Our thoughts are with the people of Nepal, as well as those visiting the country at the time of this disaster," the company said.
It recommended customers sent texts if possible to ensure minimal impact on Nepal's mobile networks.
Vodafone said it would also credit local customers' calls and texts to Nepal.
The offer applied to mobile, residential and business calls made to landlines and mobile phones in Nepal.
The retrospective Vodafone credit would apply to calls and texts made from 5pm on Saturday to 5pm today, New Zealand time.
Matt Williams, Vodafone's consumer director, said the earthquake had crippled infrastructure in the region, as well as destroying homes and communities.
"We are also mindful of New Zealanders with loved ones in Nepal or with close ties to a nation we've shared so much with in the past,' he said.
Mr Williams urged customers to use text to stay in touch with family and friends in Nepal, so that traffic on heavily congested local networks can be prioritised for emergency communications.