In some contexts, yes; but not in others. It depends on whether there is a good reason for the rule, or if it is a pretext to cover up discrimination on the basis of national origin.
Some rules prohibiting speaking a foreign language are permissible because they serve a legitimate purpose and are not designed to discriminate. For example, if there are a number of speakers of one particular language in a workplace, such a rule might exist to protect non-speakers of that language from being excluded, or to increase communication and safety on the job.
However, rules of this type that do not serve any purpose or that are selectively enforced may be discriminatory. For example, if a “no foreign languages” rule is applied to Chinese speakers but not Spanish speakers, that could well show discrimination against persons of Chinese origin, since the rule obviously isn’t important enough to be enforced against everyone. An employer policy which requires employees to only speak English, even in their most private moments in the lunch room or on a break or on a personal call, is likely to be unlawful unless the employer can show a legitimate purpose for such a broad policy.
Think you’ve been subject to discrimination? Contact the Hayber, McKenna & Dinsmore.