The disease affects nerves and leads to fatigue, muscle problems and loss of vision.
Preliminary data from trials of 732 people showed that ocrelizumab slowed the onset of disability by 24% over the course of 12 weeks.
The MS Society said the findings were a "big moment" in treating the disease.
There are two main forms of MS - relapsing remitting, which comes in a cycle of flare-ups and relapses, and primary progressive, which is a gradual deterioration.
In both forms the immune system attacks the layer of myelin that surround nerves. It acts like the insulation around a cable to allow electrical signals to be passed down the nerve fibre.
Ocrelizumab depletes a part of the immune system in order to protect the myelin.
Data presented by the pharmaceutical company Roche at the European Committee for Treatment Research in Multiple Sclerosis suggested the pace of the disease could be slowed.
Prof Gavin Giovannoni, one of the researchers involved in the trial at Barts and The London School of Medicine and Dentistry, told the BBC News website: "These are very significant results, the drug is effective and the safety profile is very good.
"It's not going to fix the damage, it's going to slow the accumulation of more damage. We don't want to raise false expectation that it will reverse disability."
He said there was now an onus on Roche to "keep the price down" so patients could benefit.
Nick Rijke, from the MS Society, said: "These phase 3 trial results will provide a great deal of hope for people with primary progressive MS.
"Finding effective treatments for multiple sclerosis is our number one priority and this is a big moment.
"So far only the top line results from this trial have been announced, so we look forward to seeing the full details with great anticipation."
The first drug to slow the decline in patients with primary progressive multiple sclerosis has been reported at a conference.