No, there is no such requirement. However, more physicians may want to use computers for submitting and receiving transactions (such as health care claims and remittances/payments) electronically, once the standard way of doing things goes into effect.
The Administrative Simplification provisions of the HIPAA law were passed with the support of the health care industry. The industry believed standards would lower the cost and administrative burdens of health care, but they needed Government's help to get to one uniform way of doing things. In the past, individual providers (physicians and others) have had to submit transactions in whatever form each health plan required. Health plans could not agree on a standard without giving their competitors a market advantage, at least in the short-run. The law, which requires standards to be followed for electronic transmission of health care transactions, levels the playing field. It does not require providers to submit transactions electronically. It does require that all transactions submitted electronically comply with the standards.
Providers, even those without computers, may want to adopt these standard electronic transactions, so they can benefit directly from the reductions in cost and burden. This is possible because the law allows providers (and health plans too, for that matter) to contract with clearinghouses to conduct the standard electronic transactions for them.