The Department of Agriculture, Fisheries and Forestry said it was looking into the reports.
Wellard said Sindh Livestock Department officials undertook the culling after local police forced employees and stockmen from PK Livestock to leave an abattoir.
"Because they had been removed from the site by police, Wellard and PK Livestock staff were unable to prevent the cull from occurring," Wellard said in a statement.
"We are concerned by the Sindh Livestock Department slaughter method because it is inconsistent with Wellard's animal welfare ethos and our multi-million dollar annual investment in improving animal welfare."
Wellard said it was concerned by "the fabricated health concerns" used as a reason to kill the livestock.
The company said the culling stopped on Saturday when it was granted a court injunction.
Karachi-based The News cited Wellard managing director Steve Meerwald as saying he had not eaten or slept since he had seen the "gruesome" video of the slaughter.
"Regardless of whether they were healthy or not, the way they were killed or buried alive is neither humane, nor Islamic," Mr Meerwald told The News.
Animals Australia said the reports were disturbing.
Its campaign director Lyn White said the events in the Middle East in the past month had proved that exported animals faced unacceptable risks.
"What Australian sheep have endured in Pakistan is unforgivable but the reality is that the only way to ensure such a terrible situation is never repeated is to end our participation in this cruel and unnecessary trade," Ms White told AAP.
- AAP