Kravchenko had allegedly been told to "get rid of" the journalist
Mr Kravchenko had been due to testify on Friday in the case of murdered journalist Georgiy Gongadze. Initial reports say he committed suicide.
President Viktor Yushchenko has pledged to find out who abducted and killed Gongadze, who reported on high-profile corruption scandals, five years ago.
He said those involved had a choice of testifying or "sentencing themselves".
Ukraine's prosecutor general said on Wednesday that investigators knew who had killed Gongadze, but have not made the name public.
The discovery of his headless body in a wood near Kiev triggered a political scandal, especially after the emergence of a covertly-recorded tape that allegedly implicated the former President, Leonid Kuchma.
GONGADZE CASE Sept 2000 - Abducted. Headless body is found weeks later Jan 2001 - Tape recordings apparently implicating President Kuchma emerge Feb 2001 - EU calls for murder inquiry May 2001 - US forensic tests confirm headless body is Gongadze's Dec 2004 - Viktor Yushchenko elected president, promises to solve case 1 March 2005 - Suspected killers arrested
In the tapes, Mr Kuchma was heard to complain about Gongadze's reporting and allegedly ordered Mr Kravchenko to "get rid of" the journalist.
Mr Kuchma has repeatedly denied the allegations, and says the tapes have been edited to distort his words.
But correspondents say it is difficult to see how the case will not now reach him.
According to Ukrainian law, the former president has no immunity against criminal prosecution.
He is currently on holiday in the Czech Republic, and is expected to return home next week.
Communist MPs have called for his arrest.
Suicide or murder?
Mr Kravchenko had been summoned to give evidence to prosecutors at 1000 local time (0800 GMT), but was found dead an hour earlier at his home in the exclusive Kiev suburb of Konche Zaspa.
Kravchenko was found dead at his home outside Kiev
He had a gun in his hand, and officials say his death was probably suicide. But several media reports say he had more than one gunshot wound.
Gongadze's widow, who fled to the US after her husband's murder, said Mr Kravchenko's death was part of a cover-up.
There were "too many people from the old regime who would try to conceal the true course of events", she told AP news agency.
The former minister had been under surveillance since December and was barred from leaving Ukraine, according to media reports.
Two of Gongadze's alleged killers are interior ministry policemen who have been detained.
A proper investigation into this crime was among the main demands of the pro-Western opposition, which staged the "orange revolution" that brought Mr Yushchenko to power following the disputed elections in November.
"Everyone has a choice," he said on Friday. "Either co-operate with the tribunal, the prosecutor, give testimony ... defend your rights and honour. There is a second possibility - sentence yourself."
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Yuri Kravchenko,  ex-Ministro do Interior da Ucrânia foi encontrado morto, na sua casa, apenas horas antes de ser interrogado a respeito do caso do jornalista assassinado Georgiy Gongadze. Os primeiros relatos indicam que ele se suicidou, mas as circunstâncias da sua morte resultarão provavelmente em mais  investigação por parte das autoridades.

Yuri Kravchenko foi o Ministro do Interior da Ucrânia em 2000, quando o sr. Gongadze foi assassinado. O corpo descabeçado de  Gongadze foi enterrado numa floresta nas redondezas de Kiev.  Sua cabeça nunca foi encontrada.  Até agora ninguém foi preso  por causa do assassinato.  Acreditava-se que Kravchenko poderia fornecer evidências para alguma detenção.