Officers issued the image of a hooded man wanted in connection with a knife incident in Little Wratting.
One person wrote: "A man with eyes... Not too many of them around." Another said police were hunting "Darth Vader".
The police said e-fits were "helpful" and the victim gave a detailed description of the man's eyes and hood.
The artist's impression was released on Monday after a man was threatened with a knife in the town on Saturday morning.
The suspect is described as a white man, aged in his late 30s to early 40s, around 5ft 10in tall, of skinny build with blonde hair.
A Suffolk Police spokesman said: "The victim was able to describe in detail the offender's eyes, style of cap, hooded top and scarf worn across his face."
He added some people have "come forward" since the e-fit appeal.
But some, posting on the force's social networking site Facebook page, thought the picture was "a wind-up".
Dozens of people commented, including one who wrote: "You'll never catch a ninja" and a number of people suggested it was "a waste" of the artist's time.
Dr Samantha Lundrigan, senior lecturer in criminology at Anglia Ruskin University, in Cambridge, defended the e-fit.
"Assuming that the facial features that are portrayed are accurate, then this man may well be recognisable to those that know him," she said.
"As the e-fit clearly shows the suspect's eyes and some of his eyebrows, it is possibly not quite as useless as it first appears."
A Suffolk police e-fit showing only the eyes of a suspect has been described as "a ninja" and "a joke" on the force's Facebook page.