The draft legislation, published today, seeks to create two new offences relating to behaviour which can "incite religious, racial or other forms of hatred" in and around football grounds and on the internet.
If approved, the Offensive Behaviour at Football and Threatening Communications (Scotland) Bill, will mean bigots will face up to five years in prison and the prospect of a football banning order.
Existing law sees people who disrupt football matches charged with breach of the peace, which carries a maximum one-year sentence.
However the Bill includes behaviour deemed to be threatening, abusive, disorderly or offensive.
Online hate crime, such as abusive or offensive comments posted on Twitter, is also included and carries the same five-year maximum jail term.
Speaking on BBC Radio Scotland, Community Safety Minister Roseanna Cunningham said: "This Bill is a fairly short, sharp Bill, which is creating two new criminal offences, one of which is directed very much at activity in and around, and related to, football matches but not absolutely confined to the grounds, and the second offence will deal with the problem of the threatening communications which we began to see an upsurge in a couple of months ago.
"The Bill is a direct response to what we saw happening towards the end of the football season and that is why we want to have it in place before the start of the new football season."
The Offensive Behaviour In Football And Threatening Communications Bill could be passed by MSPs before they go on summer recess.
It comes in the wake of several high-profile football-related incidents.
Recent problems have seen two men appear in court after suspected parcel bombs were sent to Celtic manager Neil Lennon and two other high-profile supporters of the club in March.
Ms Cunningham added: "This is only a piece of legislation dealing with a very ugly manifestation of it (sectarianism) we saw in Scotland in the last few months.
"Sectarianism in the wider sense will take a great deal more work right across the board and that work will be continuing."
Concerns have been raised that the legislation is being rushed through the Scottish Parliament.
Church of Scotland Moderator the Reverend David Arnott said: "Whilst we are not against the ideas in this Bill, we remain unconvinced of the wisdom of this approach.
"The speed at which it is being rushed through means it appears to lack scrutiny and clarity."
However, Ms Cunningham said ministers felt they had to move quickly to deal with the issue.
She said: " We saw a very ugly situation developing towards the end of the last football season, very ugly - an image of Scotland going around the world which we really, really do not want to see continuing.
"We felt as a Government that we had to move fast to tackle some of that in its specifics while we dealt with the broader problem throughout society."
Scottish Football Association chief executive Stewart Regan welcomed the Bill.
He said: "In particular, we are pleased to see that it covers sectarian and other forms of unacceptable chanting and threatening behaviour.
"As we approach the start of a new season, it is important we look forward with anticipation and excitement. Football is this country's national sport and we all have a responsibility to ensure that entertainment replaces aggravation and that a family atmosphere is generated inside our grounds instead of a hostile one.
"As part of our new strategic plan, the SFA has developed a Scotland United philosophy and it is our wish that everyone involved in the game in this country - the league bodies, supporters, clubs and media - embraces that ethos."
However, the Law Society of Scotland said the Bill is being pushed through Parliament too quickly and that the resulting lack of scrutiny may create legislation that is open to successful challenge.
Bill McVicar, convener of the society's criminal law committee, said: "We understand the importance of tackling sectarianism. This is a very serious issue and one that needs both attention and action from our political leaders.
"However, it is because of the importance of this issue that the Scottish Government needs to allow adequate time to ensure the legislation can be properly scrutinised.
"It is particularly vital for sufficient time to be allowed at stage one, the evidence gathering stage, for proper public consultation."
