The vessel was intercepted by Israeli naval ships off the coast of Gaza and forced to head south, the charity which chartered the ship said.
The charity, headed by Col Muammar Gaddafi's son, said it wanted to reach Gaza, but would not risk violence.
In May, Israeli forces clashed with another convoy, killing nine on board.
On Monday, an Israeli military inquiry said it had found mistakes were made at a senior level during the operation, which sparked international outrage, but the troops had been justified in using force.
The Libyan-chartered Amalthea left Greece on Saturday, carrying food and medical equipment, as well as 15 pro-Palestinian activists and 12 crew members.
Egyptian officials at El-Arish, some 50km (30 miles) to the west of Gaza, said the ship docked at the north Sinai port late on Wednesday.
By Malcolm BrabantBBC News, Athens
According to the ship's owner, Alex Angelopoulos, the Amalthea did not suffer a mechanical breakdown - the story about engine failure was a ploy, invented by the Cuban captain, after the Israelis surrounded the vessel and gave him an ultimatum to change course away from Gaza.
The captain was trying to buy some time for the Libyan charity to muster international diplomatic support to pressure the Israelis to let the vessel through. He restarted the engines around midday local time and is now underway.
Mr Angelopoulos earlier said this expedition was a risky venture, although he prided himself on taking chances.
He said he was motivated by humanitarian reasons, but he is also acting in the tradition of Greek shipowners like Aristotle Onassis, who made fortunes by breaching embargoes.
"As soon as the ship arrives in El-Arish, Egyptian authorities will unload its cargo and hand the aid to the Egyptian Red Crescent, which will deliver it to the Palestinian side," Egypt's Foreign Minister Ahmed Abul Gheit said earlier.
The vessel was intercepted by Israeli navy boats some 100km (60 miles) off the coast of Gaza and blocked from heading any further towards the east.
An Al-Jazeera correspondent on board said that Israeli navy boats had formed a "wall" on one side of the Amalthea and forced it towards El-Arish.
Israel's navy began shadowing the vessel overnight, after warning that it would not be allowed to break the naval blockade of Gaza.
The Amalthea resumed its voyage mid-morning on Wednesday after idling for a few hours in international waters.
The Israeli military said the ship had run into engine trouble, but the ship's owner later told the BBC that it was a ploy by the captain to buy time for the Libyan charity to muster international support.
A spokesman for the Gaddafi Foundation said those on board would not resort to violence.
"First and foremost, we want to arrive in Gaza," Yussef Sawani told Al-Jazeera TV. "If this is impossible, we don't want to subject anyone to danger."
Israeli officials denied the group's reports that they were given an ultimatum to change course by midnight or face a forceful takeover.
Banned items:
Restricted items:
Source: Israeli ministry of foreign affairs
Guide: Eased Gaza blockade
The 92m (302ft) Amalthea, renamed Al-Amal (Hope) for the mission, is loaded with 2,000 tonnes of food, cooking oil, medicines and pre-fabricated houses, the group says.
For the past three years, Israel has enforced a tight economic blockade on the Gaza Strip, only allowing in limited humanitarian aid.
It says this is necessary to stop weapons for Palestinian militant groups inside Gaza being smuggled in, and to put pressure on the Islamist movement Hamas, which controls the coastal territory.
Egypt has also closed its border with Gaza, only opening it occasionally.
The blockade, maintained by Israel and Egypt, was widely described as "collective punishment" resulting in a humanitarian crisis for Gaza's 1.4 million people.
Last month, Israel announced it would ease restrictions by allowing consumer goods into the territory while banning or restricting trade in weapons and materials that could have a military use.
Meanwhile, Israel's parliament voted on Tuesday to strip an Israeli Arab lawmaker of some key privileges for joining the flotilla of aid ships that tried to break the Israeli blockade of Gaza in May.
The Knesset decided to remove Hanin Zuabi's diplomatic passport and funding for legal defence.
Some MPs complained that by penalising an Arab member, the parliamentarians were endangering democracy, but others said that it was her actions which threatened freedoms and rights in Israel.
Ms Zuabi, an MP with the left-wing Arab nationalist Balad party, said the Knesset was punishing her out of vengeance and was threatening co-existence between Jews and Arabs.
A ship loaded with aid supplies for Gaza has docked in an Egyptian port, ending the latest attempt by activists to break Israel's Gaza blockade.