The decision to discontinue operations followed an "extensive review" of the business.
Renishaw said it had tried to find a collaboration or acquisition partner for the diagnostics unit but had not received any acceptable offers.
Renishaw Diagnostics (RDL) was spun off from Strathclyde University in Glasgow.
It develops technologies to detect infectious diseases in humans.
In a stock market announcement, Renishaw said: "We continue to look at opportunities for the sale of RDL assets and to support employees in finding alternative employment.
"We would like to express our thanks to the employees of RDL for their considerable efforts since the company was formed in 2007."
In a separate development, Ayrshire-based Lamar Group Ltd, which supplied materials and products to the UK printed circuit board industry, has been placed in provisional liquidation with the loss of 11 jobs.
Provisional liquidators Johnston Carmichael said cheaper competition from China had had "a profound impact" on the UK circuit board manufacturing industry, with more than 90% of production shifting to the Far East.
Donald McNaught, restructuring partner at Johnston Carmichael, said: "Lamar Group has been a very well-run business and retains a portfolio of valuable assets - the management team has been proactive in trying to head off the impact of cheaper Chinese manufacturing, but ultimately they have recognised there is nothing more they can do.
"Despite several attempts to diversify into new markets the business has been unable to stop the decline in sales volume. We're actively seeking buyers for the assets which remain."
Precision engineering group Renishaw is to close its diagnostics unit in Glasgow, with the loss of up to 33 jobs.