The Chelsea defender retweeted criticism of the former England striker and Match of the Day pundit after he called for the left-back to be omitted from the next Three Lions squad
On the highlights programme, Shearer called for Cole to be omitted from Roy Hodgson's national squad for the upcoming World Cup qualifiers against San Marino and Poland after the left-back labelled the Football Association "a bunch of t****".
Those comments came in response to the publication of the judgment that banned Cole's Chelsea team-mate, John Terry, for four matches for racially abusing QPR defender Anton Ferdinand. Cole gave evidence as a witness, but his credibility was called into question by the FA's Independent Regulatory Commission.
The 31-year-old hit back at Shearer by retweeting a comment that read: "Alan Shearer says [Ashley Cole] needs to be banned for comments. I want his opinion on bans for kicking Neil Lennon in the head. #GlassHouses"
Shearer escaped punishment despite appearing to kick the Celtic manager and former Leicester City midfielder in 1998. It was speculated at the time that, as England captain, the Newcastle United player was treated leniently with the World Cup in France looming.
"I think the FA can put a big statement out here by actually not fining him [Cole] but actually banning him on Friday [for England] against San Marino,'' Shearer said. "Because we've seen players fined £50,000, £60,000, £70,000. That's not a deterrent to them.
"Stopping them from playing football will be a deterrent. If they do it quickly - which they haven't done in the case, which has taken 14 months - if they do it in four to five days, I think it puts a big statement out to the rest of the players.''