I would refactor the code to:

class Service1
  def self.foo
    new.foo
  end

  def foo
    puts 'foo'
  end
end

class Service2
  def bar
    3.times.each do 
      Service1.foo
    end
  end
end

And would then use a spec like this

describe "#bar" do
  let(:service1) { class_double("Service1") }

  it "calls Service1.foo three times" do
    expect(service1).to receive(:foo).exactly(3).times

    Service2.bar
  end
end

You can achieve this by mocking new method

class Service1
  def foo
    puts 'foo'
  end
end

class Service2
  def bar
    3.times.each do 
      Service1.new().foo
    end
  end
end

Then the test:

let(:mocked_service) { instance_spy Service1 }

it "calls Service1.foo three times" do
  allow(Service1).to receive(:new).and_return mocked_service

  Service2.bar

  expect(mocked_service).to have_received(:foo).exactly(3).times
end

However, as mentioned in the comment - the necessity of using mocks is a first sign of flawed OO design, meaning that the problem you posted is merely a symptom. Refer to SOLID principles to find better design.