The 29-year-old full-back must serve a two-match ban imposed by the Scottish FA for his disciplinary misdemeanours while playing for Hearts.
Neilson will miss Swansea's visit to the Walkers Stadium on August 8 and the trip to Ipswich on August 15. The suspension only applies to league games so he will be eligible for the Carling Cup first round tie at Macclesfield in between.
A Scottish FA spokesman said: "His last caution on May 12 took him to 18 points, which is a one-game ban. And because he also amassed 18 points during the 2007-08 season, that warrants another one-match suspension.
"The suspension came into effect on May 26, which was 14 days after his last offence by which time the Scottish season had ended. The Football Association in England has already contacted us to confirm the situation."
Neilson made his first appearance for Leicester in last weekend's 1-1 pre-season friendly draw at Tamworth before the squad flew to Slovenia for this week's training camp.