Visitors have been stuck in the mountain resort for two days after snow blocked road and rail links.
Zermatt's official site had said that the first train to the nearby village of Tasch would leave at 11:15 am (10:15 GMT), but later announced that the resumption of service had been pushed back.
"The railway cannot operate at 11.15 am as planned due to the difficult removal of snow between Tasch and Zermatt", the statement said.
"The persons in charge are working hard on the reopening and are confident to open the railway in the afternoon," it added.
Tasch is a small Swiss village six kilometres from Zermatt that serves as a gateway for those travelling in the Matterhorn mountain region.
The network in Tasch remains closed due to snow, but replacement buses are operating, making it possible for people to reach regional airports.
Extreme weather has caused havoc in several Swiss areas, including the Valais region south of Zermatt and in the canton of Bern, where a World Cup downhill training run had to be cancelled due to snow and high winds.
- with AFP