There has been no communication since then and a farmer who went to Mr Olbs aid was shot at and retreated.
President Robert Mugabe is due to broadcast a televised address at 1200 local time (1100GMT) in which he is expected to give a definitive response to the worst political crisis in the country's history.
The president has cancelled three days of official anniversary celebrations, saying the money saved will be used to help victims of recent floods.
Political tension has exploded into violence in recent days, amid the occupation of white-owned farms by supporters of the government.
On Tuesday, farmer Martin Olbs was trapped and wounded on his farm in Nyamandhlovu near Zimbabwe's second city of Bulawayo in the south-west of the country.
Another farmer, David Stevens, was shot dead at the weekend. At least five other opposition activists have been killed in recent weeks.
Surrounded
Martin Olbs telephoned a neighbour early on Tuesday, first saying his farm house had been surrounded by 30 to 40 veterans and it "looked pretty serious".
"He phoned later to say he had been shot and could we call an ambulance," the neighbour said.
There has been no communication since then and a farmer who went to Mr Olbs aid was shot at and retreated.
The farmer said the security fence had been cut and an ambulance chartered to fetch the wounded farmer had not been able to reach the house.
Local police said: "We received a report and sent a team to investigate, but we don't have details yet."
Mac Crawford, the head of the Commerical Farmers' Union in the Bulawayo area, told the Zimbabwean paper the Daily News that the government had been arming the veterans in his area.
He said there had been numerous sightings of weapons, but offered no proof of the government's involvement.
Regrets
On Monday, President Mugabe told white farmers that he regretted the death of Mr Stevens - whose land had been occupied.
One of the farmers' leaders said Mr Mugabe had spoken of getting the situation back to normal, but had not promised to order the squatters to leave.
Mr Stevens was shot dead and two opposition workers killed in a petrol bomb attack on Saturday, in the worst violence since President Mugabe's supporters began occupying white-owned farms last month.
In addition to the killings, several farmers were severely beaten, and black farm labourers' homes burnt down.
The Zimbabwe National War Veterans Association, which is co-ordinating the illegal occupations, has made it clear it has no intention of calling off its followers.
Liberation songs
Mr Mugabe's speech is expected to clarify the government's position, and also announce a date for parliamentary elections.
He has previously said voting would take place in May.
Zimbabwean television has been broadcasting a programme of popular Zimbabwean music in the run-up to the presidential address - which was originally scheduled for earlier on Tuesday morning.
Many of the singers wore combat uniforms and brandished automatic weapons as they sang lyrics commemorating the struggle against white rule in the then Rhodesia.
Meanwhile, the Nigerian Foreign Minister, Sule Lamido, has gone to Harare to mediate in the land dispute.
Britain, the former colonial power, had asked Nigeria to help persuade Mr Mugabe to end the land occupations.
Nigerian President Olusegun Obasanjo "would be prepared and willing" to intervene in the current crisis between Britain and Zimbabwe, his spokesman said.
He recalled how the Nigerian leader facilitated a meeting between Mr Mugabe and British Foreign Secretary Robin Cook during recent EU-Africa summit in Cairo, Egypt.
The land occupations have continued in defiance of two High Court rulings. Police have said they do not have the resources to evict squatters.