At least two of the incidents involved attacks on children.
On Thursday a seven-year-old, who was attacked in the face by a family Jack Russell in East Herringthorpe, Rotherham, required surgery to their lips.
On Tuesday a two-year-old was attacked by a neighbour’s pocket bully in Ecclesfield.
Meanwhile police were called to a property in Bolton-Upon-Dearne at 05:00 GMT on Monday after a family dog, a pocket bully, savaged a man’s face, leaving him with life-altering injuries.
Officers were called to the Fox Hill Road area of Sheffield on Thursday after a woman walking her dogs was aggressively approached and attacked by a loose Staffordshire bull terrier.
The dog was captured by police.
A spokesperson said: “These incidents are a stark reminder that such attacks are preventable – and that responsible dog ownership is not optional, it’s essential.”