Jean Campbell, 53, was last seen heading towards Cranhill Park while walking her dog Kai on Friday, December 13. Her body was found by her husband at around 7.40am the next day.
As reported in later editions of yesterday's Evening Times, an appeal for information about her murder appeared in the newsfeed of up to 200,000 Facebook users in the Glasgow area yesterday.
It came as charity Crimestoppers offered a reward of £5000 for crucial information.
Throughout the day the site had more than 10,000 hits, police said.
Detectives are now trawling through the comments in a bid to gather new information.
Speaking at the scene yesterday, Detective Chief Inspector Colin Carey, from Police Scotland's Major Investigation Team, said: "Social media is an excellent way to reach thousands of people who can sometimes be hard to reach.
"We are keen to exploit this opportunity to obtain more information regarding this murder."
More than 1000 DNA samples have been taken from people - both men and women - in the Cranhill area.
Police have stepped up patrols in a bid to reassure residents.
Mr Carey added: "I really do believe that there is someone out there who is harbouring the person responsible or knows who is responsible.
"This can be for a number of reasons, fear or intimidation being the most obvious."
Speaking last night, a police spokesman said: "The comments will be looked at and the Facebook campaign will continue as will other communication and information campaigns over the course of the investigation."
Anyone with information can contact police on 101.