The legislation, passed within a fortnight of it first being tabled, further threatens the China-ruled city's freedoms, critics say
No militant group has claimed responsibility for the attacks but both Islamic State (IS) and the Taliban militants operate in the area, which borders Pakistan.
Gulzada Sangar, a government health official in Jalalabad, said no deaths were reported in the blasts, which struck as the country marked the 100th anniversary of its independence.
An IS suicide attack on a crowded Kabul wedding hall killed 63 people on Saturday.