The photo of the weapon hanging from a door was sent to five MPs on Twitter
South Yorkshire Police said two people had been arrested yesterday afternoon in connection with the tweets.
The tweet was sent last week from an account named Sheffield and Yorkshire Direct Action Brexit Group.
A spokeswoman for the force said: “A 40-year-old-man and a 33-year-old woman were arrested in Sheffield on suspicion of sending malicious communications. Enquiries are ongoing.”
The tweet was addressed to MPs Anna Soubry, Chuka Umunna, David Lammy, Angela Smith and Sarah Wollaston - all of whom have backed calls for a second referendum on leaving the EU, including the option to remain in the union.
The biography section on the Twitter page read: “We need to leave the EU and the politicians are not listening.
“We want to start a movement to help as many people as possible have their voice heard. Help us.”
The pinned tweet described the group as “a new movement for the poor and the working class who are so often overlooked and ignored”.
The tweet added: “We run this country, it’s time the politicians remembered that!”
Angela Smith’s office declined to comment on the tweets.
Twitter said it does not comment on individual accounts for reasons of privacy and security.
The offending tweet was yesterday removed from public view and it is understood Twitter placed the account in a read-only state until the user took action to delete the message.
Twitter states that it has a ‘zero tolerance policy against violent threats’, with anyone deemed to be sharing such messages facing ‘immediate and permanent suspension of their account’.
More than 150 people commented on the message before it was removed from public view - with many saying they had reported the matter to police.
Responding to criticism, a later tweet from the account insisted the crossbow message was not intended to be threatening.
The follow-up tweet declared: “Threatening to kill?????? How? All used to protect my home and my family, just indicating that whatever happens with Brexit, when law and order goes to **** I and my ‘terrorist network cell’ (you’re an idiot) will be ready! Will you?”
A further tweet from the account stated: “I’m a caring kind of person. Just want my MPs to be careful that nothing happens to them.”
And another said: “It’s OK, don’t bother wasting your energy. Everyone has reported me and.....shock horror......no police....no Twitter ban.”