"Vote Leave will be suspending major campaign events tomorrow such as the planned rally in Birmingham," in central England, a spokesman for the Brexit camp said, adding however that low key campaigning like leafleting was likely to continue.
A spokesman for the official "Remain" camp, Britain Stronger in Europe, meanwhile, said that its campaign would also "continue to be suspended tomorrow".
The murder of opposition Labour MP Cox yesterday in her northern English constituency brought an abrupt halt to a bitter and divisive campaign over whether Britain should stay in or leave the European Union.
Many MPs are also likely to be unavailable for campaigning on Monday, when parliament is being recalled to allow colleagues to pay tribute to Cox.
Len McCluskey, the general secretary of Britain's biggest trade union, Unite, had earlier cancelled a major speech in favour of the EU planned for Monday.