Kyl also said that the move would send a negative message to former Soviet satellites who have expressed support for the West in recent years.
"This will be a bitter disappointment, indeed, even a warning to the people of Eastern Europe," he said.
The reaction came after the US informed the Czech Republic and Poland on Thursday that the missile plan laid by the administration of George Bush, Obama's predecessor, had been abandoned.
Russia had called the plan to build a radar base in the Czech Republic and place interceptor missiles in Poland a direct threat to its national security.
Obama's decision is a concerted move away from Bush's defence policy and the White House said its new plan was aimed at providing stronger and more mobile defence of the US and its European allies.
Al Jazeera's Rob Reynolds, reporting from Washington DC, said the Republican opposition to Obama's plan was to be expected.
"I think the reaction has been quite predictable. Generally, the Republicans have called this a show of weakness and of appeasement towards Russia and Iran," he said.
"On the other hand the Democrats are supportive - Carl Levin of the Senate Armed Forces Committee said Obama had made 'a sound choice that improves [US] security and the decision opens the door to missile defence co-operation with Russia', which Levin says would send a powerful message to Iran."
The Obama administration has downgraded the apparent threat posed by Iranian missiles.
The US and Europe have repeatedly accused Iran of seeking to enrich enough uranium to build nuclear weapons while Tehran has consistently said that its nuclear programme is aimed at generating electricity.
Buck McKeon, the senior Republican on the House Armed Services Committee, said that Obama's decision proved that the White House "does not recognise the threat posed by the Iranian regime", which the Bush administration had given as a reason for the planned missile shield.
He also said that the Obama administration's move would be interpreted by Russia as weakness.
"I am concerned that the administration is heading down a path where it is willing to undercut our allies and cave to Russian demands on vital national security matters," he said.