Two people have been arrested on suspicion of sending malicious communications over the disappearance of Nicola Bulley.
Lancashire Police said it received reports over the weekend of messages being sent to Wyre Council members.
A 49-year-old man from Manchester and a 20-year-old woman from Oldham have been arrested on suspicion of malicious communications offences.
The man has been bailed pending further inquiries until May 12 while the woman remains in custody.
On Monday, Wyre Council removed councillors’ contact details from its website due to “inappropriate emails and phone calls” about Ms Bulley’s disappearance.
It said it had temporarily removed contact details for “parish and town council members” after Lancashire Police confirmed its investigation.
Wyre Council leader Michael Vincent said: “We appreciate the emotional gravity of the situation; however we will not tolerate any form of abuse of any of our elected members of Wyre Borough Council or any of the town and parish councils within our borders or our staff.
“The community has shown great strength and resilience during the investigation, and we urge everyone to continue to show compassion and empathy.
“It is a shame that we have had to take this step at such a difficult time and appropriate steps are being taken to ensure that residents are still able to contact their elected representatives.”
The council added: “Wyre Council will log any reports of abuse and these will be forwarded to the police. Please be respectful.”
Chief executive Garry Payne said: “Everyone is deeply saddened by the ongoing Nicola Bulley case and our thoughts are with the family and friends.
“We are supporting Lancashire Police where required and we urge everyone to remain respectful at this time.”
A force spokesman said: “We received reports at the weekend of a number of malicious messages having been sent to Wyre Council members.
“Inquiries led to the arrest of a 49-year-old man from Manchester, on suspicion of malicious communications offences. He has since been released on bail, pending further inquiries, until May 12.
“A 20-year-old woman from Oldham has also since been arrested on suspicion of malicious communications offences and she remains in police custody. inquiries are ongoing.”
Ms Bulley, 45, vanished on January 27 in the village of St Michael’s on Wyre while walking her springer spaniel Willow after she dropped her two daughters, aged six and nine, at school.
She has not been seen since.
Police believe the mortgage adviser fell into the River Wyre in a “10-minute window” between 9.10am and 9.20am that day.
The search for her continues and on Thursday detectives extended it to the sea after they said finding her there “becomes more of a possibility”.