"The ministry will talk to the highest officials within the German government to obtain clarification and express its concern over the fact that the German office of export controls gave its green light to the contract," foreign ministry spokesman Arye Mekel told AFP.
"The German government's decision is contrary to the spirit of the sanctions imposed by the UN Security Council against Iran," he added.
Israel has long called on the West to ratchet up its sanctions regime to try to persuade Iran to halt its enrichment activities, which Israel and the United States believe are aimed at developing nuclear weapons. Tehran has denied seeking atomic weapons and insisted its nuclear drive is purely aimed at generating electricity for a growing population.
The Simon Wiesenthal Centre on Wednesday urged German Chancellor Angela Merkel to block the €100-million ($156-million) deal between Germany's Steiner and the Iranian government for plants that would produce 10,000 barrels of gas per day.
No one was available for comment at Steiner's headquarters on Thursday.
The German Export Control Office said the rift had been sparked by a "misunderstanding." Spokesman Holger Beutel said the deal was for "an exportation of goods that are not of a controversial nature." Because of this, he said, neither the Export Control Office nor the German government had to give its authorization.
He said the office had only reviewed in February whether official approval was necessary and concluded it was not. Germany is one of Iran's biggest trade partners. Its exports to Iran totalled €3.6 billion last year.
Berlin is working with Western powers to convince Tehran to abandon sensitive nuclear work. It has reduced export guarantees with Iran, and German banks have largely ceased doing business with the Islamic republic over its nuclear programme.
French energy giant Total had won a contract for work at Iran's sprawling South Pars gas field including the construction of a gas liquefaction plant that Tehran intended to use for energy exports. But in early May, the group announced it would suspend investing in Iran because it was politically too risky.
Israel, the region's sole if undeclared nuclear armed power, considers Iran its greatest threat.