The patient died at Russells Hall Hospital in Dudley on Saturday.
It means 745 people have now died at the hospital after contracting Covid-19. Across the Black Country, Birmingham and Staffordshire 7,617 people have died with the virus in hospitals.
A further 1,482 people have died in the region's care homes.
The UK-wide death toll, which only includes deaths within 28 days of a positive test, increased by three to 127,907 on Monday.
Separate figures published by the Office for National Statistics show there have been 153,000 deaths registered in the UK where Covid-19 was mentioned on the death certificate.
The Government also said that, as of 9am on Monday, there had been a further 7,742 lab-confirmed cases in the UK.
Government data up to June 13 shows that of the 71,672,208 jabs given in the UK so far, 41,698,429 were first doses - a rise of 147,228 on the previous day.
Some 29,973,779 were second doses, an increase of 181,121.