Desire Nyaruhirira had been a top adviser at the Rwandan embassy in Burundi for many years.
The expulsion comes amid worsening relations between the east African neighbours.
Last week, Burundi accused Rwanda of training rebels seeking to destabilise the country, allegations it denies.
The Burundian official, who told the BBC Great Lakes service why Mr Nyaruhirira had been expelled, requested not to be named.
Rwanda has not commented on the expulsion.
The move by the Burundian government is a sign that the time for restraint is over, says the BBC’s Prime Ndikumagenge from the capital, Bujumbura.
Relations between the two countries have been strained since Burundi’s president Pierre Nkurunziza decided in April to run for a controversial third term in office, a decision Rwandan president Paul Kagame criticised.
They deteriorated further after Burundi accused Rwanda of hosting failed coup leader Gen Godefroid Niyombare, who tried to seize power in May.
Burundi has been hit by a spate of assassinations and attempted assassinations since Mr Nkurunziza won disputed elections in July.
About 70,000 Burundians are living in refugee camps in Rwanda after fleeing the unrest.
Pierre Nkurunziza and his Rwandan counterpart Paul Kagame were once on good terms, even playing football together when they visited each other’s countries.
This changed in November 2012, when the two disagreed sharply over the M23 rebel group in eastern Democratic Republic of Congo. Mr Nkurunziza opposed the M23, which, according to the UN, had Rwanda’s backing.
The two leaders clashed at a meeting of regional leaders over the issue, prompting Mr Nkurunziza to walk out before the talks ended.