At least 10 of the plotters had been arrested, but the top suspects were still on the run, the minister said.
The coup was to have been staged on 8 October, with an attack on the presidential palace, he added.
Forces loyal to the ex-president staged a coup in September 2015, but surrendered a week later after protests and opposition from top generals.
French-educated banker Roch Marc Kabore was elected president in November, ending a turbulent period since Mr Compaore's overthrow in a popular uprising in 2014. The latest coup plotters had also planned to attack a prison to free those held over last year's coup, Interior Minister Simon Compaore said at a press conference in the capital, Ouagadougou.