Chantal Ramazani, who is now in hiding, believes the intention was to block Mr Katumbi's bid for the presidency in elections due in November.
President Joseph Kabila is required by the constitution to step down this year but no poll date has been set.
The intelligence services deny the accusations.
Africa Live: More on this and other stories
Last month, Mr Katumbi was convicted of illegal property selling and sentenced to three years in prison, in absentia.
The 51-year-old businessman, owns one of Africa's biggest football clubs, is currently out of the Democratic Republic of Congo (DRC) seeking medical treatment.
In a letter addressed to the president and other politicians and organisations, Judge Ramazani says the facts against Mr Katumbi were never examined in tribunal.
She claims the purpose of the trial was cripple Mr Katumbi's political future and that she was threatened with losing her job, even imprisonment, if he were not convicted.
After sending the letter, she went into hiding.
The BBC's Maud Jullien, in the Congolese capital Kinshasa, says Mr Katumbi is seen as a favourite in the race for the presidency and is expected to return to the country before an opposition rally on Sunday.
Opponents of President Kabila say he is trying to stall elections to stay in power, but the constitution states he must stand down after his two terms in November.
Moise Katumbi was governor of the south-eastern Katanga province for almost a decade.
In September last year he broke ties with the ruling party when he accused President Kabila, his former ally, of wanting to cling to power.
His popularity is partly down to his job as the president of a great source of Congolese pride - football club TP Mazembe.
They are Africa's reigning football champions, having won the African Champions League for the fifth time in November.

Dons manager Derek McInnes and assistant Tony Docherty opted to stay with Aberdeen despite talks this week with Championship club Sunderland.
"I was fairly confident he would stay," Milne told BBC Scotland on Friday.
"He phoned yesterday morning and said he was absolutely committed to the club. It would have been a massive wrench for him to walk away."
McInnes, 45, took over from Craig Brown in 2013 and the following year led the club to League Cup success, beating Inverness Caledonian Thistle in the final for the Dons' first trophy in 19 years.
Last season, McInnes and Docherty guided the Dons to second place in the Premiership behind Celtic, and were runners-up to Celtic in the Scottish Cup and League Cup.
"He sees Aberdeen Football Club as his," said Milne of McInnes who, along with Docherty, is contracted to the Pittodrie club until 2019.
"I've built up a very close relationship with Derek over the last three or four years and we have been in constant dialogue over the past four or five days. I believed it was 50-50 (whether he would leave).
"He has always said how happy he is at Aberdeen. He feels he gets the backing of the board, he has been very successful here, any move entails risk and he knows what he's got here.
"Last year was probably the best season in the last three decades and he believes that he can better last year.
"I'm absolutely delighted. I've always said we had one of the best management teams in the whole of the UK here."
Milne revealed that the club had "reshaped" McInnes's contract in the "past week or so" and that fans can expect to see a few new players coming to Aberdeen when McInnes returns to work on Tuesday.
Milne also says he would be surprised if the club don't make a few signings before the end of next week.
A judge in the Democratic Republic of Congo has said she was pressured by the intelligence service to convict opposition politician Moise Katumbi.
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Aberdeen chairman Stewart Milne thinks the club have retained "one of the best management teams in the UK".