The explosion happened at about 2325 BST. Police were told in a call to a Belfast hospital about an hour earlier that a vehicle had been abandoned.
Officers were en route to the station, which is staffed on a part-time basis, when the explosion happened.
The two people's injuries are not life-threatening. Shots are reported to have been fired before the explosion.
The two people who were treated in hospital - a man and an elderly woman - are said to have been left "extremely shaken".
BBC reporter Chris Page, who is in the town, described debris littering the main street with damage caused to a pub, shops, houses and a community centre.
He said the extent of the damage to the police station is not yet clear.
He added that local people believe the quick action of firefighters, who moved people from their homes, had prevented further injuries.
Police have said the bomb is believed to have been in a white Toyota Corolla and detectives have appealed for anyone who saw it being abandoned at the station, or beforehand, to contact them.
'High threat'
The attack came as security sources told the BBC the threat posed by dissident republicans in Northern Ireland was higher than at any time since the Omagh bomb almost 12 years ago.
The explosion was reportedly heard up to 10 miles from the scene.
The town centre has been cordoned off and Newtownhamilton High School has been opened for residents who have had to leave their home.
Northern Ireland's first and deputy first ministers have issued a statement condemning the attack.
Peter Robinson said it was "cowardly and evil" while Martin McGuinness said those responsible had nothing to offer "but hardship, division and pain".
Ita Gibney, who runs the local community centre, said it was very upsetting for people in the town.
"It's going to be a couple of days before we're going to get into the community centre to see what's happened in it, to see what sort of damage has occurred there," she said.
"We just want this place to run as normal."
Last week, the Army defused a car bomb outside the town's police station, one of a number of attacks on police and security bases in Northern Ireland, including an explosion at Palace Barracks in Holywood.
Meanwhile, a pipe bomb has exploded behind a house in Chestnut Hill in the Brackaville area of Coalisland, County Tyrone at about 2330 BST on Thursday night.
A man and a woman, who were in the house at the time, were uninjured but a number of windows were damaged.
Maybe Jimmy can confirm this??
Yet again though Armagh has been hit and, sadly, this will receive very little news coverage and will be hushed-up and swept below the carpet so as to uphold this facade of 'peace'. It will be forgotten about, but I have friends in Armagh and if you were to speak to them they'd tell you how things really are ... only two months ago one of them buried their elderly mother, and because they had served in the British Army/Security Forces, they couldn't even use their own church for the funeral and after being contacted by the police they had no alternative but to go to another church some miles away. Their catholic friends and neighbours whom they'd known for a lifetime couldn't attend the funeral and had to go secretly to the graveside, the family couldn't invite mourners back for tea, the funeral needed a police escort and a police helicopter flew overhead for the duration and republican flags and tri-colours were flown and nailed to telegraph poles along parts of the route simply to antagonise ... all this at the funeral of an elderly lady whose only crime was that her family served the Crown, and a number of them were murdered. I know this happened because it was my friend's mother
This and other such incidents continue, but even people over here don't get to hear about them ... it's all covered up and doesn't even get reported on our local news channels. Occasionally it gets a mention on the local Radio, but that's about it.