The PA's civil affairs authority had on Sunday accused Hamas of "summoning, arresting and abusing our employees", leading it to conclude that their presence was futile, according to official Palestinian news agency WAFA.
An AFP journalist saw Hamas officials at the border crossing's main gate and inside accompanying offices in southern Gaza on Monday.
A Hamas border official, speaking on condition of anonymity, said they had taken control "to avoid a vacuum".
Rafah -- the only way for Gazans to leave their enclave that bypasses Israel -- was closed Monday due to the Orthodox Christmas holiday but it was not clear whether it would reopen as scheduled on Tuesday.
Hamas' interior ministry spokesman Iyad al-Bozum said his organisation "will protect the interests of our people."
Islamist movement Hamas seized control of Gaza in 2007 in a near civil war with Palestinian president Mahmud Abbas' Fatah party.
But the Palestinian Authority took control of Rafah in November 2017, as part of a deal for Egypt to reopen a border that had been entirely shut from August that year and largely sealed for years before that.
There was no immediate comment from Egypt about whether its side of the crossing would be open Tuesday.
The PA's taking control of Rafah in 2017 was seen as a first step towards implementing a reconciliation agreement between Hamas and Fatah.
The deal has subsequently broken down and Abbas' PA has taken a series of measures against Gaza.
Egypt has allowed the border to be open regularly since August 2018, providing a lifeline to the enclave's two million residents.
Israel has maintained a crippling blockade of Gaza for more than a decade, in a bid to isolate Hamas and keep it from obtaining weapons.
Critics say the policy amounts to collective punishment.
Israel and Hamas have fought three wars since 2008.
A planned event commemorating the anniversary of the founding of Fatah -- due to take place in Gaza on Monday -- was cancelled on Sunday, as organisers said they faced threats.