She started her formal cricket training in the Karnataka Institute of Cricket in 2005 when she was 13. Realising her talent, the institute’s director Irfan Sait urged Veda’s father to shift her to Bengaluru to further hone her skills. The youngest daughter of a cable operator, her father moved from a small town in Karnataka’s Chikkamagaluru to Bengaluru to help realise his daughter’s dream of playing for the country one day. She was initially trained at Karnataka Institute of Cricket at Bengaluru.

She made her debut in international cricket at the age of 18 in a one day international against England Women at Derby in June 2011 and went on to score 51 runs in that match. Meanwhile, her T20 debut for India was in a match against Australia in the Natwest T20 Quadrangular series at Billericay, on the same tour of England.

In November 2015, she was named in B-grade contract list, this was first time BCCI offered contracts to women players.

Karnataka State Cricket Association hosted their first-ever Twenty20 exhibition match between a KSCA President’s XI and a KSCA Secretary’s XI and Veda was chosen to lead the President’s XI. In October 2017, she was signed by the Hobart Hurricanes for the 2017–18 Women’s Big Bash League season.

In February 2018, she became the youngest player for India Women to score 1,000 runs in WODIs, during the third WODI against South Africa.

In October 2018, she was named in India’s squad for the 2018 ICC Women’s World Twenty20 tournament in the West Indies. In January 2020, she was named in India’s squad for the 2020 ICC Women’s T20 World Cup in Australia.