Swansea magistrates said Robert Riley's online messages were also racially and religiously aggravated and that only a custodial sentence could be imposed.
Riley, from Port Talbot, was sentenced to eight weeks in custody after admitting posting an abusive Twitter message about the death of Leeds schoolteacher Ann Maguire.
The 42-year-old was the second person to be charged with the offence in the wake of the death of Mrs Maguire, who was stabbed to death in her classroom at Corpus Christi Catholic College last month.
Yesterday a third person was arrested in Cardiff and bailed.
More top news
Showers overnight will make way for heavy rain tomorrow! The Met Office has issued a warning to be aware!
Dermatology services in west Wales are at breaking point say top skin experts in Wales. Hywel Dda currently has no consultant dermatologist.
Sara Garbutt of Rhyl robbed a vulnerable pensioner and stood by while he was beaten up. She's now been jailed for eight years.