"This was the work of Islamic Jihad, an organisation financed and working for Iran, and we consider the Syrian government responsible for the firing and it will suffer the consequences," the army said in a statement.
It was referring to a Palestinian militant group which is based in the Gaza Strip.
The rocket fire came as Mohammed Allan, a Palestinian detainee who Islamic Jihad says is one of its members, ended a two-month hunger strike over his detention without trial by the Israeli authorities.
Prime Minister Benjamin Netanyahu and Defence Minister Moshe Yaalon visited northern Israel on Tuesday to meet military officials.
Israel seized 1,200 square kilometres (460 square miles) of the Golan from neighbouring Syria in the 1967 Middle East war and annexed it 14 years later, in a move never recognised by the international community.
Since the Syrian conflict erupted in 2011, the Golan has been tense, with a growing number of rockets and mortar rounds hitting the Israeli side, mostly stray, prompting occasional armed responses.