The government statistics, which cover the period up to May 16, also show that 62.4 per cent of people in the borough have had at least one dose.
In terms of the town of Melton Mowbray, one third of residents have had both doses (9,056 people) and 57 per cent have had at least their first.
Both vaccinations have been given to almost half of all adults living in the Rutland and Melton parliamentary constituency area, with 85 per cent having had at least one jab.
The figures for the Leicester, Leicestershire and Rutland area reveal that 37 per cent of adults are now fully vaccinated and two-thirds of adults have had at least their first dose.
The statistics reflect a recent focus on giving second jabs to the most vulnerable people and those working in frontline health and care roles.
In comparison, the percentage of people having a first jab have increased very slowly in the last month, from 29,870 to 31,207 in the borough of Melton and from 14,793 to 15,473 in the town of Melton Mowbray.
Latest Covid vaccination figures (covering December 8 to May 16):
1st dose - 31,207 (62.4% of all residents).
2nd dose - 17,818 (35.6% of all residents).
MELTON MOWBRAY town
1st dose - 15,473 (56.9% of all residents).
2nd dose - 9,056 (33.3% of all residents).
LEICESTER, LEICESTERSHIRE AND RUTLAND
1st dose - 600,420 (67.4% of all adults).
2nd dose - 327,012 (36.7% of all adults).
RUTLAND AND MELTON CONSTITUENCY AREA
1st dose - 65,473 (84.6% of electorate).
2nd dose - 36,268 (46.9% of electorate).
MELTON BOROUGH LOCAL NEIGHBOURHOOD AREAS
1st doses with 2nd doses in brackets:
Melton Mowbray North 5,395 (3,118);
Melton Mowbray West 4,992 (2,929);
Melton Mowbray South 5,086 (3,009);
Bottesford/Harby/Croxton Kerrial 6,454 (3,524);
Asfordby/Frisby/Old Dalby 4,601 (2,669);
Waltham/Wymondham/Great Dalby 4,679 (2,569).