Sharma, who represents Tezpur constituency in Assam, rode a white horse, with a placard that read: “Pollution Free Vehicle”.
Delhi’s northeast MP Manoj Tiwari pedalled his way on a bicycle to parliament.
Former Delhi state BJP president Vijay Goel protested against the odd-even curbs by putting out posters and stickers on his SUV against the scheme.
On Monday, several BJP lawmakers, including actor-turned politician Paresh Rawal, violated the odd-even traffic curbs on four-wheelers by commuting in their even-numbered vehicles on the odd date.
Rawal later apologised to Delhi Chief Minister Arvind Kejriwal.
Members of parliament are not exempted from the restrictions on four-wheeler use in the Delhi government’s odd-even scheme which came into effect for the second time on April 15. The city government has arranged for buses to ferry the MPs, but not many members are opting for these.