The arrest, which drew about 100 Hamas gunmen to the detainee's aid, followed a night of clashes between a new Hamas-led security force loyal to Prime Minister Ismail Haniyeh and Palestinian police deployed by rival party President Mahmoud Abbas.
The fighting, which began overnight at a Gaza police station, ended in a gun battle and injured four people, Reuters reported.
Tensions have been high in the occupied territories since January when Abbas' Fatah Party lost in elections to Hamas, launching a power struggle between the parties' leaders.
Abbas blames the militant Hamas group for putting an armed security force of 3,000 men on the streets in a direct challenge to his government. Abbas has responded by upping the number of police in Gaza by the thousands, Reuters reported.
Palestinians, many of whom were forced to flee the streets Friday, fear continued clashes could result in civil war, according to Reuters.
On Friday, Secretary of State Condoleezza Rice called the Middle East situation "dangerous" and expressed support for Abbas.
"It's a very tense situation and one that we hope will be resolved," she told reporters. "We obviously believe that president Abbas, who we believe has the confidence of the Palestinian people, should be able to exercise his responsibilities as president of the country."
The U.S. has led an international effort to cut off funding to the Palestinian Authority since Hamas, whose charter calls for the destruction of neighboring Israel, came to power.
Hamas refuses to detract its stance. "We will not take any step in the direction of recognizing the legitimacy of the occupation on the Palestinian land," Haniyeh has said.
Abu Zuhri, the official detained at the Gaza crossing, claimed the money he was attempting to bring in was donations from other Arab countries to the Palestinian government. Palestinian border guards confiscated the money pending an investigation into its source.
Meanwhile, an unidentified U.S. official told Reuters that President Bush is expected to urge Israel to soften its stance on removing settlements from part of the West Bank, but permanently maintaining key settlements in other areas. The United States fears such a strategy could derail peace efforts.
Aids to Israeli Prime Minister Ehud Olmert are expected to meet with Abbas next week, Reuters reported, in the highest level talks between the two governments since Hamas' victory.