Dorino Manzin told a news conference that death threats were also sent to the participants in next year's annual gay pride parade.
Defence Ministry spokesman Mate Radeljic told Hina the ministry was investigating the case, which he said the ministry condemned.
He added the public would be informed once the investigation was over.
Manzin said the threats were not a case of violation of human rights but an act that undermined Croatia's security system. He added it was in the ministry's interest to find the perpetrator so that the ministry would not appear to be a homophobic and aggressive institution with omissions in the security system.