Complaints originating from social media make up "at least half" of calls passed on to front-line officers, a senior officer has told the BBC.
Chief Constable Alex Marshall, head of the College of Policing, said the number of crimes arising from social media represented "a real problem".
He said it was a particular problem for officers who deal with low-level crimes.
About 6,000 officers were being trained to deal with online offences, he said.
He said the police and public were still trying to understand when online insults became a crime.
Mr Marshall told BBC Radio 4's Law in Action: "As people have moved their shopping online and their communications online, they've also moved their insults, their abuse and their threats online, so I see that it won't be long before pretty much every investigation that the police conduct will have an online element to it.
"It's a real problem for people working on the front line of policing, and they deal with this every day.
"So in a typical day where perhaps they deal with a dozen calls, they might expect that at least half of them, whether around antisocial behaviour or abuse or threats of assault may well relate to social media, Facebook, Twitter or other forms."
'There's a line'
A number of front-line police officers from different parts of the country spoken to by the BBC agreed with Mr Marshall's assertion that a significant amount of the calls they were asked to respond to were now related to social media, including death threats, bullying and harassment.
Det Con Roger Pegram, from Greater Manchester Police, said the way offences were committed had changed a lot since he joined the force 14 years ago.
"These are traditional offences," he said.
"You don't need to actually front someone up face-to-face in the street to threaten them.
"This can all be done from the comfort of your own home, a coffee shop with wi-fi, and these people can commit crime anywhere to anybody."
One officer, who did not wish to be named, said while there were serious complaints worthy of further investigation, many related incidents not considered crimes in the era before social media.
He said: "A lot of the time.. it's that whole attitude of, 'I don't know what to do, I'll call the police, they'll sort it out for me.'
"It should be a case of let's be sensible, let's not be friends with that person on Facebook, perhaps contact Facebook first or don't use Facebook. It's common-sense stuff."
Mr Marshall agreed that the police "couldn't possibly deal with every bit of nonsense and disagreement that occurs in social media".
"People throughout history have shouted abuse at each other and had disagreements and arguments and possibly said things that they regret later and the police have never investigated every disagreement between everyone," he said.
"So we have to be careful here that there's a line that needs to be drawn and if something is serious and it's a crime and someone is genuinely threatened or in the case of domestic abuse - maybe they're being coerced and treated deliberately in this way as a sort of punishment by a partner - that's a serious issue that we need to take on."
Public education required
Mr Marshall said a combination of police training, public education and enforcement by social media companies was required to combat the problem.
Although the director of public prosecutions's guidance was a "good starting point", Mr Marshall said, 6,000 officers were being trained over the next few months by the College of Policing - which sets all police standards in England and Wales - to make judgments about when a complaint identified a pattern of behaviour that required further investigation.
And while anecdotal evidence from officers indicates that dealing with complaints arising from social media now absorbed a significant amount of their time, it is not yet borne out in the figures.
Currently, online crimes are recorded under traditional headings such as harassment or threats to kill and not as a cybercrime, so each record is required to be read individually to ascertain if the crime originated on social media.
Mr Marshall said because of that, the force was missing out on information.
The College of Policing was currently carrying out research to quantify how many crimes actually originate on social media, he said, and was expecting the results in the next couple of months.
The Home Office said that it had introduced a voluntary "flag" this year that would enable forces to highlight online crime "to further improve our understanding of where crime occurs".
This is expected to become mandatory by 2015/16.