Figures from TNS Worldpanel for the 12 weeks to May 20 reveal the grocer's growth is the highest since the Safeway takeover.
As part of a£450 million investment over three years, Morrisons is set to overhaul its stores, replace its logo and accelerate store openings.
After the news that Kwik Save closed 79 of its 182 stores this week, the retailer represents just 0.2 per cent of the grocery market.
Asda and Sainsbury's both recorded strong growth of 8 per cent year-on-year and have added 0.3 share points against a year ago.
Tesco's growth rate is still ahead of the market average at 7 per cent, lifting its market share to 31.3 per cent compared with 31.1 per cent last year.
Somerfield's market share dropped to 3.8 per cent from 4.2 per cent the year before with a drop of 4 per cent year on year.
Both co-operative groups and independent grocers are matching the market growth rate, which is 6 per cent year on year and are retaining their market share at 4.5 per cent and 2.8 per cent respectively.