The drawing shows a fair-skinned man with thick, medium-length black hair, dark eyes, a wispy beard and black-framed glasses.
People have pitched in to predict and guess what the suspect would look like if he altered his appearance, such as by not wearing glasses, shaving his head or changing his hairstyle.
Art designer Witcha Suyara posted on Facebook that his friends had asked him to develop his impressions of the suspect in case he disguised himself.
"I hope my design skill will help police catch the guy faster," he said.
StickboyBangkok tweeted "Alternative photofits of #Bangkok bomber without glasses, with short hair & wearing a cap (Pic Anamisis Zaki)" with the image of the suspect in different looks.
Footage from surveillance cameras is being used to chase the suspect. For example, CSI LA Page on Facebook posted a video of the suspect riding a tuk-tuk and asked people to find the tuk-tuk driver who picked up the suspect.
Agence France-Presse also reported that Thais had taken to the Internet to crowd-source the identity of the prime suspect in the shrine bombing.
Netizens went into overdrive after police on Tuesday released a grainy security recording of a man appearing to place a bomb-laden backpack at the crowded shrine a few minutes before the blast.
On social media, Thais have been using the hashtag #bombercluephoto to collate images taken in the area where the bomb exploded.
"All camera around there before bomb. Please share and hashtag," Thai Twitter user @Kemkrithera wrote in English.
The report also mentioned that other Internet sleuths had focused their search on locating where that T-shirt could be bought.
One post, written by Thai Facebook user, Sa-nguan Khumrungroj, featured an Internet search for a very similar-looking T-shirt available in Indonesia.
"This shirt is sold in Indonesia," he wrote.
"I've seen this [for sale] in Pratunam," replied a friend, referring to a large garment market in Bangkok.
However, while the suspect is still at large, there are many falsely accused.
People who bear a resemblance to the suspect have posted their pictures and said they were not the suspect, just a look-alike.
Wisawa Bossbibi Suwannakul said on Facebook that the sketch seemed to be him, but just looked like him. It is not him.
After that, he decided to delete the post, saying he realised that the picture that compared him and the suspect in the sketch might be used in both proper and improper ways.