The suspect entered the pharmacy on Falls Road at around 9.30am, where he threatened the owner and a locum before attacking them, the Police Service for Northern Ireland (PSNI) said.
PSNI confirmed that a man in his 40s sustained a stab wound to his arm, while a second sustained a wound to his chest. Their injuries were not believed to be life-threatening, PSNI added.
Read the owner's account of the attack below.
Police also confirmed a 26-year-old suspect had been detained at the scene on suspicion of offences – including attempted murder and attempted robbery – and is currently in custody.
A spokesperson for the Pharmaceutical Society of Northern Ireland said there is a “recognised drug problem” in Belfast – and Northern Ireland more widely – and prescription drugs “seem to be part of the problem”.
He added that there have been “several” attacks on pharmacies in west Belfast "in recent times".
Sheelin McKeagney, chair of Pharmacy Forum Northern Ireland, said he would be talking to police and the Department of Health about how pharmacists can improve their personal security.
Mr McKeagney said the attack was “shocking” and would have been a traumatic experience for the members of staff.
Police are appealing for witnesses to the attack and have asked anyone with information to contact detective sergeant Michael Hawthorne at Musgrave Police Station by calling 101 and quoting reference number 249 of 06/04/17, or calling Crimestoppers anonymously on 0800 555 111.