"Everyone is safe and sound, so that is the good thing," southern operations manager Richard Gray said.
He said it was too early to say why the collapse happened, and the focus was now on making as much of the site operational as quickly as possible.
About 12 tonnes of water is made into steam per hour on site and piped around the many buildings to power plant and machinery.
Neighbours reported hearing a single loud boom about 1.50pm, followed by the sound of steam escaping from the ruptured pipes, a noise which continued for about 30 minutes.
Fonterra chief operating officer global operations Robert Spurway said the silo was one of about 100 on site and represented less than 10% of Edendale’s total capacity for raw milk storage.
The silo appeared to have failed and the subsequent collapse damaged a nearby pipe bridge, creating the loud noise heard by those in the vicinity.
"Whilst some of the damage may take several weeks to repair, the situation is under control and we are now working to get the plant back up and running as normal," Mr Spurway said.
There was no explosion, he said.
Milk collection in Southland could be temporarily affected by the incident and Fonterra would keep farmers informed about the situation.
A Fire Service command unit from Invercargill and fire crews from Edendale, Wyndham, Mataura, Gore, Kingswell and Invercargill attended.
Firefighters wearing breathing apparatus could be seen entering a building immediately to the south of the collapsed silo.
State Highway 1 runs past the plant, which stands in the middle of the Edendale township.
Police cordons were set up to divert motorists away from the township.
A nearby resident, who did not want to be named, said the silo which collapsed was a raw milk silo which fed into the D4 milk drier, the newest drier at the site.
The boom was the steam pipe gantry hitting the ground and the loud noise was high-pressure steam escaping from the pipes.
Tania Bal, who owns the dairy across the road from the plant, said she heard a single loud boom before the electricity went off momentarily.
She heard a siren sound at the plant, and went outside to see black smoke and flames coming from a chimney.
The smoke and flames quickly subsided.
Workers could be seen leaving the site in ones and twos.
They said they had been instructed not to speak to the media.
Milk tankers were prevented from entering the site and about a dozen could be seen parked on nearby streets.
Mr Gray said most night shift workers were told to remain home last night.
He did not know when when plant would begin receiving milk again.
