The journalist who was shot, Julius Odeke, is now unconscious in a local hospital, his sister has told the BBC.
He had apparently refused orders to get out of a vehicle carrying opposition MP Nandala Mafabi in the eastern district of Budadiri, where a heavy military presence has been reported.
"They shot the journalist in the ribs, we have left him in casualty," Mr Mafabi told NTV Uganda.
At a press conference after polls closed, the police said there had been some isolated incidents of violence in the east.
A Red Cross official told the BBC that about 70 people had been injured in that part of the country.
Polls closed at 1700 local time (1400 GMT), but voters still queuing to vote were allowed to do so. Results are due to be declared within 48 hours.
The European Union's chief observer said he was generally happy with what he had witnessed.
"We are glad to observe that no significant violence has taken place and the process is done in a peaceful manner," said Edward Scicluna.
Earlier, the BBC's Joshua Mmali at a polling station in Kampala said that after polls opened 45 minutes late, the queues quickly died down.
Many people said they did not have confidence in the process but had gone to cast their ballot so they could say they had done their duty, he said.
"I came early to vote and then I have to keep witnessing the process. We fear rigging," voter Badru Busulwa told the AFP news agency.
After a lavishly funded campaign, Mr Museveni is seen as the favourite.
There have been complaints from some people who said they registered to vote but were unable to find their names on the roll.
According to Uganda's Daily Monitor newspaper, independent presidential candidate Samuel Walter Lubega discovered that his name missing when he went to vote at a polling station in Kampala.
Despite the omission, electoral officials allowed him to cast his vote.