The first of the four separate attacks happened on Monday, with the latest on Saturday afternoon.
The offences in Birmingham and Solihull are not linked, but have raised fears about knife crime in the area.
David Jamieson, the region's police and crime commissioner, said knife crime was a "major concern and has been for quite some time".
Timeline of attacks:
Mr Jamieson said: "There has been a growing trend that's particularly prevalent in the warmer weather, The warm weather does bring out more crime, particularly crime that happens on the streets.
"It's desperately worrying. Any increase in any violent crime is worrying.
"The police are there to tackle the violence so people will have the full weight of the law thrown at them."
Elsewhere, a 19-year-old man was arrested on Saturday in connection with a stabbing at Merry Hill shopping centre in Brierley Hill at about 11:15 BST.
A man was injured and taken to hospital for treatment.
Four men have died in a week of stabbings in the West Midlands.