Restrictions on marriage between a Mauritian and a non resident?

Those on student visa cannot get married, otherwise that will cause an influx of immigrants in the country. This is not only applicable in Mauritius but also in most countries around the world.

The Civil Status Division says it clearly on their website. I quote what is relevant here:

1. Work/Residence permit (applicable to expatriates)
2. Proof of financial means (Contract of employment or recent bank statement or recent salary slip).
3. The non-citizen should be the holder of a valid marriage visa issued by the Immigration Office.

Hope that helps.