President Abdel Fattah al-Sisi, who called for tougher laws following the assassination of his top prosecutor last week, is expected to approve the law within days.
The cabinet has already approved the draft law.
Article 33 of the draft law, published in several Egyptian newspapers, stipulates a minimum two-year sentence for "reporting false information on terrorist attacks that contradicts official statements".
The law also opens up the possibility of deportation and house arrest.
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Zind said the law was prompted in part by coverage of Islamic State group attacks on Egyptian soldiers in the Sinai Peninsula on July 1.
The military spokesman said 21 soldiers and more than 100 militants were killed in the attacks and ensuing clashes, after security officials said dozens more soldiers had been killed.
The government has accused foreign media who reported the higher death toll of exaggerating troop casualties.
"The day of the attack in Sinai some sites published 17, then 25, then 40, then 100 dead," Zind said.
"There was no choice but to impose some standards," he said. "The government has the duty to defend citizens from wrong information."
"I hope no one interprets this as a restriction on media freedoms. It's just about numbers (in death tolls)," he said.
"If the army says 10 died, don't report 20."
The country has been fighting a jihadist insurgency in Sinai since the army, then led by Sisi, overthrew Islamist president Mohamed Morsi in 2013.
The attacks have killed hundreds of policemen and soldiers, while more than 1,400 people, mostly Morsi supporters, have been killed in a crackdown on protests.