The Scot, whose own sexuality drove him to try to take his own life, said Uganda's new laws which impose harsh penalties for same-sex relationships had "appalled right-minded people around the world".
He also called on the organisers of the Commonwealth Games, which begins on July 23, to inform the legislation's architects they are "not welcome in the VIP boxes of this country".
The cyclist, who is also the first sporting champion in Scotland to come out as gay, has urged Glasgow 2014 chairman, Lord Smith of Kelvin, not to welcome Ugandan politicians.
It is unclear whether the country's president, Yoweri Museveni, will be in Glasgow during the Games either or both of Uganda's sports ministers, Jessica Alupo or Charles Bakkabulindi, will attend.
Obree has also launched a petition entitled No Hate at the Games calling for Uganda to be snubbed by Lord Smith and Glasgow 2014, which by yesterday evening was approaching 1000 including signatories from Australia, South Africa, the USA, Sweden, France, Germany and the UK.
Obree's intervention comes days after the Scottish Government said it would offer sanctuary to Ugandans persecuted under the laws passed last week by President Museveni which include life sentences for gay sex and same-sex marriage.
The country had already outlawed same-sex relations but the new law allows life imprisonment as the penalty for acts of "aggravated homosexuality".
A day after the law was enacted a Ugandan newspaper published a list of what it called the country's 200 top homosexuals, including some who previously had not identified themselves as gay.
Despite international condemnation of laws in Russia banning the "promotion of non-traditional sexual relations" ahead of the Winter Olympics in Sochi, laws in Uganda and other Commonwealth countries are arguably more severe.
Forty of the 53 member nations have some kind of law persecuting same sex relationships.
Obree said: "Life for gay people in Uganda is downright scary. Hate lists with names and faces of gay people are on the front page of newspapers, they're being beaten while they go to the shop, stalked in the streets in broad daylight, and even killed. And now the new anti-gay bill just passed is set to make it much, much worse.
"Let's make these Games not only an event which rightly celebrates the sacrifice, skills and supreme efforts of the athletes and representing nations, but one where we take a stand against those who stir up hate.
"In days, Lord Smith and the organising committee of the 2014 games will begin inviting dignitaries. Let's call on them to make sure that Ugandan politicians who backed this bill are off that list, and tell them they are not welcome in the VIP boxes of our country. Let's let Lord Smith and his organising committee know that Uganda's decision to pass this bill has appalled right-minded people around the world."
A Glasgow 2014 spokeswoman said: "Every Commonwealth Games Association (CGA) participating in the Glasgow 2014 is wholly responsible for extending invitations to their appropriate dignitaries, including their sovereign or head of state, sports minister and high commissioner.
"CGAs are also responsible for ensuring their guests are compliant with the Commonwealth Games Federation's protocol guidelines for each nation and territory. The Glasgow 2014 Organising Committee is not responsible for issuing invitations to the Commonwealth Games to foreign dignitaries."
The Scottish Government reaffirmed its position on equality and said a Pride House would be on offer for gay athletes.