The center will include senior ministers and military and police chiefs and will be designed to respond quickly to situations that could have a "strategic impact", chief security minister Luhut Pandjaitan told reporters.
"We hope this will be (operational) as soon as possible," he said.
Since coming to power in 2014, Widodo has placed maritime security for the Indonesian archipelago high on his government's agenda.
Indonesia has voiced fears that a surge in piracy in the waters between Indonesia and the Philippines could reach Somalian levels and has told vessels to avoid danger areas.
Up to 18 Indonesians and Malaysians have been kidnapped in three attacks in recent weeks on tugboats in Philippine waters by groups suspected of ties to the Abu Sayyaf militant network.
Abu Sayyaf, which has posted videos on social media pledging allegiance to Islamic State militants in Iraq and Syria, has demanded 50 million pesos ($1.1 million) to free the hostages, but the Indonesian government has said it does not intend to pay the ransom.