The book Machine Learning (1997) by Tom Mitchell covers case-based reasoning (CBR), a form of instance-based learning (nearest neighbor is the typical example of IBL) in chapter 8 (p. 230).
T. Mitchell writes
Instance-based methods such as $k$-NEAREST NEIGHBOR and locally weighted regression share three key properties. First, they are lazy learning methods in that they defer the decision of how to generalize beyond the training data until a new query instance is observed. Second, they classify new query instances by analyzing similar instances while ignoring instances that are very different from the query. Third, they represent instances as real-valued points in an $n$-dimensional Euclidean space. Case-based reasoning (CBR) is a learning paradigm based on the first two of these principles, but not the third. In CBR, instances are typically represented using more rich symbolic descriptions, and the methods used to retrieve similar instances are correspondingly more elaborate. CBR has been applied to problems such as conceptual design of mechanical devices based on a stored library of previous designs (Sycara et al. 1992), reasoning about new legal cases based on previous rulings (Ashley 1990), and solving planning and scheduling problems by reusing and combining portions of previous solutions to
similar problems (Veloso 1992).
He then goes on and gives the example of a CBR system: the CADET system. He also formulates CBR as a learning problem and uses the term "learn" to refer to a search process that CADET goes through, which is similar to what k-NN does.
He then writes
To summarize, case-based reasoning is an instance-based learning method in which instances (cases) may be rich relational descriptions and in which the retrieval and combination of cases to solve the current query may rely on knowledge-based reasoning and search-intensive problem-solving methods.
To conclude, yes, CBR can be considered a machine learning technique (if you also consider k-NN a learning algorithm, which people often do), even though it may rely on knowledge-based reasoning and search-intensive problem-solving methods.
You may also be interested in the paper Representation in case-based reasoning (2005) by Ralph Bergmann et al. Moreover, the famous AIMA book (3rd edition) mentions case-based reasoning in chapter 19 (p. 799), which is dedicated to knowledge and learning.