The policemen, in plain clothes, were approached by two disguised gunmen. When the officers challenged them four shots were fired, hitting one officer in the foot. It happened just outside an intensive-care unit where the politician and his wife were visiting their seven-year-old son. The IRA's Belfast brigade admitted responsibility, saying their targets had been the policemen.
It was earlier suggested the intention was to kill the policemen and then assassinate Nigel Dodds, chairman of the Rev Ian Paisley's Democratic Unionist party.
RUC assistant chief constable Bill Stewart called the attack "an incredibly cruel and evil act" and confirmed it appeared to be directed at the policemen. Hours earlier police had warned of the likelihood of IRA attacks in the run-up to Christmas.
It happened shortly after 8 pm in the Royal Children's Hospital, where Mr Dodds's son Andrew, who has spina bifida and hydrocephalus, is being treated. The hospital is part of the Royal Victoria complex, which borders on the republican Falls Road, and as such is treated with caution by loyalists and members of the security forces.
It is understood members of Mr Dodds's party had warned him against establishing a pattern in visiting the boy, and thus leaving him open to an assassination attempt.
Mr Dodds has made many television appearances as a spokesman for Mr Paisley's party. He is party chairman, a leading member of its Stormont talks team, a Belfast councillor and a former lord mayor of the city.
In their pre-Christmas warning, the RUC told the public "to be particularly vigilant in light of recent terrorist activity." Police were especially concerned that there is a threat facing the community following incidents in counties Fermanagh, Armagh and Londonderry, coupled with the discovery of terrorist munitions. Other incidents have included the discovery of mortars and incendiary devices, and an attempt to blow up a security force vehicle with a horizontal mortar in north Belfast.
Nelson McCausland, a Unionist councillor visiting another patient at the time of the attack, said he heard four shots. "It is utterly appalling that the IRA should even consider launching this attack in a children's hospital unit where one child was lying seriously ill and another child had just died."
Mr Paisley said: "It was a diabolical thing to do, to go in where a parent was seeing his sick little boy. I am absolutely sickened, yet these are the people that the British government wants me to sit down with. I earnestly pray that the prime minister will not be bluffed ... and give in to these men, who are not prepared to be democrats. This illustrates the baseness and villainy of their hearts."
Recently security has been increased for a number of public figures, some of whom are well-known Unionist politicians. The policemen accompanying Mr Dodds are not believed to be his regular bodyguards, but are thought to be stationed at Grosvenor Road RUC station, near the hospital.
Security measures are likely to be reviewed again in the light of the latest incident.