The MEP encouraged his followers to demonstrate outside the Cambridgeshire home of Michael Black and John Morgan, who recently won their civil case against a Christian B&B owner who refused to let them stay in a double room due to her religious beliefs.
Griffin's Twitter account has been since been suspended, and a spokeswoman for Cambridgeshire police confirmed it is looking into "a number of complaints" about the tweets.
Griffin had written: "If anyone can give us address of the 2 bullying 'gay' activists who've won case v Christian B&B owners, we'll hold demo...for rights of all home owners, gays included, to rent or not rent rooms to whomsoever they wish."
Two hours later, he added: "A British Justice team will come up to [their address] & give you [Black and Morgan] a... bit of drama by way of reminding you that an English couple's home is their castle. Say No to heterophobia!
"Why don't left & gay activists confront Muslims instead of picking on meek & forgiving Christians? Bullies are always cowards!"
Officers have been in contact with the men and planned to visit their home in Brampton tonight (October 18).
LGBT Labour, the party's campaign for gay rights, urged people to report Griffin for allegedly breaching the Communications Act 2003, which states that posting menacing messages online is an offence. Others have reported the comments to the Met's internet hate crime unit.
Stonewall, the gay rights campaign group, called Griffin's actions "unbelievably shocking", adding that it is a "real example of the hatred still out there towards gay people".
Susanne Wilkinson, owner of the Swiss Bed and Breakfast in Cookham, Berkshire, was ordered to pay the couple £3,600 in damages on Thursday after Reading Crown Court found that she had been directly discriminatory to them. The money will be donated to charity.