One person is in a critical condition.
Mr Trump's announcement - met with worldwide dismay - reversed decades of US policy on the sensitive issue.
Israel deployed hundreds of extra troops in the West Bank as Palestinians went on strike and took to the streets.
Protesters set tyres alight and threw stones, and Israeli troops fired tear gas, rubber bullets and live bullets.
Two rockets were fired from the Gaza Strip towards Israel but fell short, Israel's army said.
In Gaza, according to Reuters news agency, Palestinians threw stones across the border fence at Israeli soldiers who responded with live fire.
Many of Washington's closest allies have said they disagree with the move, and both the UN Security Council and the Arab League will meet in the coming days to decide their response.
There are fears the announcement could lead to a renewed outbreak of violence. The Palestinian Islamist group Hamas has already called for a new intifada, or uprising.
What has been the reaction?
Israeli Prime Minister Benjamin Netanyahu said Israel was profoundly grateful to Mr Trump, who had "bound himself forever with the history of the capital".
He also said Israel was "in touch with other countries to follow suit. I have no doubt other embassies will move to Jerusalem - the time has come". He did not name any of these countries, although the Philippines and the Czech Republic have been mentioned in Israeli media.
The mood has been very different on the Palestinian side.
The leader of Hamas, which dominates the Gaza Strip, has called for a "day of rage" on Friday and said it should "be the first day of the intifada against the occupier".
"We have given instructions to all Hamas members and to all its wings to be fully ready for any new instructions or orders that may be given to confront this strategic danger," Ismail Haniya said in a speech in Gaza.
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