The products were reportedly sold in Premier Inn, Brewers Fayre, Beefeater Grill and Table Table.
A statement from Whitbread said: "At Whitbread we take the quality and standards of our food extremely seriously and although we have continued to receive assurances from our suppliers about the meat content of our products, in line with the FSA guidance we have carried out independent tests on meat products.
"We sent 30 products to be tested and received the results of these tests yesterday afternoon (on Thursday 14th February). Two of these products tested positively for equine DNA and we immediately removed them from our menus. The two affected products were a meat lasagne and a beef burger. They will not be replaced until further testing has been undertaken and we are fully reassured of the integrity of our products.
"We are shocked and disappointed at this failure of the processed meat supply chain. As an industry it is clear we need the supply chain to deliver products to the highest standards of food integrity and quality that we and our customers expect.
"As a responsible business we shall work with the FSA to implement a robust testing regime to avoid this happening in the future."
"We would like to sincerely apologise to our customers for any concerns or inconvenience that this may cause."
The FSA is set to publish further details of the testing it requested from suppliers and operators later today.
The British Beer & Pub Association said: "We have advised our members to ensure that they have been in contact with their suppliers to receive the necessary reassurances regarding the origins of meat used as an ingredient within processed meat products.
"In light of the current focus of the FSA on determining compliance with both labelling and food safety legislation by retailers and food business operators, we have also advised that operators ensure that all audit processes have been reviewed to ensure that they are robust and any audit schedules are up-to-date, along with any necessary documentation and reports."