The independent body that advises government said misogyny should be treated in the same way as other discrimination when it is the motivation for a crime.
Campaigners welcomed the proposal, including Labour MP Stella Creasy, who called it "our moment for change".
Seven police forces in England and Wales class misogyny as a hate crime.
But this definition has not been adopted across the board.
When a crime is carried out against someone - such as assault, harassment or criminal damage - because of their race, religion, sexual orientation, disability or transgender identity, it is considered a hate crime and treated more seriously by the courts.
But campaigners have criticised the complex nature of the existing laws, and called for sex and gender to be added to the list.
The Law Commission has carried out a review into the legislation and is putting several recommendations into a consultation.
It said the "vast majority of evidence" suggested crimes were linked to misogyny.
The commission plans to make its official recommendations to the government in 2021.
People are generally attacked because an assailant dislikes something about that person - their appearance, their views, the football team they support.
What marks hate crime out is where the assailant says or does something that provides evidence they have targeted a person because of one of the five "protected characteristics".
So hate crimes often involve assaults on public-facing officials - traffic wardens, store detectives, NHS staff - where in the course of the incident the perpetrator abuses the victim on grounds of race, religion, sexual orientation, disability or transgender identity.
If sex and gender become protected characteristics in order to protect women, the same would apply.
The perpetrator's actions, or more likely the words they use, would have to evidence that they are targeting the victim on grounds of sex/gender.
The commissioner for criminal law, Professor Penney Lewis, said: "Hate crime has no place in our society and we have seen the terrible impact that it can have on victims.
"Our proposals will ensure all protected characteristics are treated in the same way, and that women enjoy hate crime protection for the first time."
Ms Creasy, Labour MP for Walthamstow, has led calls for a change in the law and secured the commission's review in 2018.
She welcomed the findings, saying they would help the criminal justice system "detect and prevent offences including sexual assault, rape and domestic abuse".
Ms Creasy added: "I now urge every woman who has walked with keys in her hands at night, been abused or attacked online or offline to come forward and be heard in this consultation.
"This is our moment for change - rather than asking women to pick a side of their identity to be protected, it's time to send a message that women should be equally able to live free from fear of assault or harm targeted at them simply for who they are."
The first force to introduce misogyny as a hate crime was Nottinghamshire Police in 2016.
Chief Inspector Louise Clarke, who leads the hate crime unit at the force, said it had taken numerous actions against perpetrators - and even where there was not sufficient evidence to support a prosecution, officers had spoken to men about their behaviour and explained the consequences.
She added: "Ultimately, this is about giving women the ability and confidence to report this behaviour.
"Many men aren't even aware that this happens and are often shocked by the extent of the issues."
The Law Commission is also currently consulting on whether ageism, being a member of an alternative subculture (like goths and punks), or homelessness should also be added to the list of hate crime motivations.
It is also wants the "stirring up hatred" offence to be reformed, so it is less difficult to prosecute and gives equal footing to all the groups it affects.
And it is recommending the extension of the offence of racist chanting at a football match to cover chanting based on sexual orientation.
The government has been contacted for a comment.
The issue was debated in Parliament's second debating chamber, Westminster Hall, in 2018. The then minister Victoria Atkins, replying to the debate, said the government needed to be careful when creating new laws that would "would inadvertently conflict with principles of equality".
She said: "Equality of protection is a crucial element of ensuring public support for hate crime legislation.
"In other words, if we were to have hate crime in relation to gender, we would have to think carefully about whether that would apply to the entire population or just to half of it."