The officers needed medical treatment after they were slashed at New Square Shopping Centre, on Wednesday morning while carrying out additional stop checks.
West Midlands Police said the officers were attacked by two men who became aggressive when approached, leaving them with slash injuries which are not thought to be serious.
However, a two men, aged 41 and 37, and a 31-year-old woman have been arrested on suspicion of attempted murder.
Witnesses described "chaotic scenes" at the shopping centre as the incident unfolded.
Writing on New Square Shopping Centre's Facebook page, Scott Jones said: "Was a chaotic scene but well handled by some brave officers," adding they were pleased members of the public were being helpful.
New Square Shopping Centre said a number of arrests had been carried out after the incident.
Others said one of the injured officers was applauded as he made his way to the ambulance.
Bobbie Adams told the Express & Star: "There were a few people standing round Hungry Horse talking about what had happened, and then we heard an officer shout can we make space for the paramedics.
"We saw the officer walk down with his head bandaged and everyone moved aside and everyone just started clapping.
"I also saw an air ambulance circling to trying to find somewhere to land."
Other shoppers also expressed their shock at the incident.
Amy Poultney, 39, from Walsall, said: "It's pretty scary for being on our doorstep. And it's sad that it's happened in new square.
"It's a rough place, but I've never known anything not that to happen, but two policemen being stabbed, it's pretty serious.
"I think it's getting more common for people to carry knives, I think, within Walsall, West Brom and Birmingham areas. I think it's getting more common, but I think it's shocking when you hear of something like this."
Another, who didn't wish to be named, said: "I saw the ambulance going away and asked what had happened, but I was shocked to find out it was two policemen being stabbed.
"It's the first time I've heard of this happening here, but there have been fights here in the past with young people.
"I hope the policemen are OK and I hope this means more security in the future here. I don't feel unsafe, but it's worrying that this happened."
Their comments were echoed by another shopper who commented: "I'm shocked to see the vest and other bits on the ground as I would never expect anything like this to happen here.
"It makes you wonder how safe the streets are when police officers are getting stabbed.
"The shopping centre is a busy one and while I've seen people messing around and arguing, I've never seen anything like this."
A video on social media showed one man and another figure being held down on the ground by a number of people.
A number of police officers in uniform and people wearing normal clothes were knelt and stood around them.
In the background, a crowd of people had formed watching the events.
In a Facebook statement, the centre said: "A serious incident has taken place this morning at the shopping centre which resulted in two police officers being injured.
"The men involved were arrested at the scene and the police officers are currently receiving medical treatment.
"We are now assisting West Midlands Police in their investigation and we will give further updates once we’re able."
West Midlands Ambulance Service (WMAS) confirmed it was called to the scene at 11.42am following a 999 call from West Midlands Police, reporting that two police officers had been assaulted.
The ambulance service said the officers' injuries were "non-serious". They were given medical treatment at the scene before being taken to hospital for further checks.
An ambulance, two paramedics officers and an air ambulance from Cosford attended.
A WMAS spokeswoman said: "Ambulance crews arrived to find two male police officers with non-serious injuries.
"They were given treatment on scene before being conveyed to hospital by land ambulance for further checks."
Reacting to the incident, Nicola Richards MP for West Bromwich East said: "It is very concerning to hear about today’s incident in New Square.
"My thoughts are with the brave police officers who have been injured in the line of duty and I wish them a speedy recovery. The perpetrators are now in Police custody.
"A Section 60 dispersal order has now been authorised in the town, meaning that the police can ask any person to leave the town if they believe that they are at risk of carrying out a crime.
"The police have also stepped up patrols in the area as a result of the incident.
"I’m in communication with the BID [business improvement district], New Square management, and the police about this horrific incident.
"But I’ve been clear, we all need to do more to make our town safe once again.
"So that we can welcome back visitors and make West Bromwich the best place to shop, work, and live."
A 21-year-old man has been detained on suspicion of wounding in that incident, while the victim's injuries are not believed to be life-threatening.