A 43-year-old man has been arrested after the alleged attack at roughly 8.45am on Friday.
Assistant chief constable Bernard Higgins said the suspect, who suffered minor cuts and bruises, is currently being assessed at a local hospital.
Police have said the incident was not terror-related and there is no risk to the wider public.
The officers, a man and a woman, were taken to the Inverclyde Royal Infirmary, with colleagues praising their “incredible bravery”.
One of the officers has since been taken to the Queen Elizabeth Hospital in Glasgow for further treatment.
Mr Higgins said the officers were assisting a partner agency when they made the call-out.
Part of Gateside Gardens in the Inverclyde town was cordoned off as officers investigated the alleged attack.
A team of forensics officers could be seen examining a section of a nearby road, where a shoe and an item of clothing lay in the street.
Deputy Chief Constable Iain Livingstone, interim chief constable at Police Scotland, tweeted: “Incredible bravery from police officers in Greenock this morning.
“All of @policescotland officers and staff thinking of them and their families. Courage, protecting their fellow citizens.”
Andrea MacDonald, chair of the Scottish Police Federation, said: “Our thoughts are with the injured officers and their families. Once again we see how difficult and dangerous a job it is.
“Police officers put themselves between other professionals and the public and dangerous individuals, sometimes with life-changing consequences for themselves and their families. We wish our colleagues a speedy and full recovery.”
Scotland’s First Minister Nicola Sturgeon tweeted: “My thoughts and best wishes for a full recovery are with the two police officers injured on duty in Greenock today.
“This is a reminder of the vital but often dangerous job our police men and women do, and what a huge debt of gratitude we owe to them.”