The device was thrown at the front door of a home in Cloona Mannor in the early hours of Sunday morning.
Stewart Dickson MLA said: “I must condemn those behind this latest attack, who somehow think this type of behaviour is justifiable.
“We must be thankful that no-one seems to have been in the property at the time of the attack, as this situation had the potential to be much worse. Those behind this attack are clearly very dangerous individuals, but we can’t allow them to drag our society back to the dark days of the past.
“I would appeal to anyone with information on who orchestrated this attack to come forward and speak to the PSNI as soon as possible.”